Authorities in the Washington area took different approaches Monday as they scrambled to stop the spread of the novel coronavirus: D.C. officials asked hundreds of churchgoers to self-quarantine, while officials in Maryland and Virginia said cases within their borders did not require such measures.

The number of people stricken with the virus rose Monday night, with three new cases reported in the District, one in Prince George’s County and two in Virginia. The number of known cases in Maryland, Virginia and the District climbed to 16.

Each case seemed to trigger its own set of repercussions.

D.C. Mayor Muriel E. Bowser (D) urged hundreds of people who were at Christ Church Georgetown on certain days in late February or early March to hunker down at home, in case they had been in close contact with the Rev. Timothy Cole, who tested positive for the virus on Saturday. One of the D.C. cases announced late Monday was linked to the church.

At least three D.C. schools closed for deep cleaning because a staff member had been exposed to Cole or the other confirmed D.C. patient. A youth soccer league canceled practice because some of its players attended those D.C. schools.

So Others Might Eat, the anti-hunger nonprofit agency, scrapped fundraisers, and an environmental film festival and some National Gallery events were canceled. Mariann Budde, the Episcopal bishop of Washington, ordered 88 churches and schools in the D.C. area to stop using shared cups during Communion, drain baptismal fonts, and skip handshakes and hugs.

And the Securities and Exchange Commission late Monday asked employees in its Washington headquarters to telework, effective immediately, amid concerns that one of its employees had contracted the virus. It was the first major federal agency to ask all headquarters employees to stay home because of the virus.

“This is an all-hands-on-deck operation,” said Maryland Gov. Larry Hogan (R), who announced that six state residents — two with flu-like symptoms — were quarantined and being tested for the coronavirus. All six had been on the same Egyptian cruise vessel as three Montgomery County residents who were diagnosed with the virus last week, though they traveled at different times.

But Hogan has not urged broad quarantines for people who were at a post-funeral reception at a Rockville senior living center with one of the Maryland coronavirus patients, or for those who attended the Conservative Political Action Conference in Oxon Hill, where an attendee later tested positive.

Officials said those cases involved fewer direct contacts with the infected people than Cole may have had at the church.

“It’s a different situation in a number of respects,” Hogan said. “This was the priest himself who was serving Communion to all of the parishioners while he was actively sick. There was more of a concern that he was potentially infecting people.”

Cole’s diagnosis also raised alarms because he had no recent overseas travel, unlike most other confirmed cases in the region.

Late Monday, Christ Church said its organist, Tom Smith, 39, had also been infected. Bowser announced that case and two others: a 77-year-old man who had attended the Biogen conference in Boston, which has been connected to several other cases; and a 79-year-old man about whom no other information was released.

Maryland officials said a Prince George’s County woman in her 50s had contracted the virus during out-of-state travel. She has had no contact with schoolchildren and is self-quarantined at home and in good condition, County Executive Angela D. Alsobrooks said.

Virginia officials said a Spotsylvania County resident in their 50s had tested positive, as had the spouse of a person who was diagnosed with the virus over the weekend. The couple had been on a cruise boat in Egypt that is believed to have been the source of other infections.

Earlier Monday, officials announced that a 60-something Arlington County resident had developed fever, a cough and shortness of breath after an international trip. The person had limited contact with other people while ill, the state health department said, and is receiving medical care and recuperating.

Also in Arlington, more than a dozen office tenants at two buildings in Crystal City — 201 12th St. and 1225 S. Clark St. — were notified by property owner JBG Smith that someone who works at one of the buildings had tested positive for the coronavirus.

JBG Smith spokesman Bud Perrone said the office tenant told employees who had interacted with the individual to self-quarantine and hired a contractor to disinfect its spaces. JBG is sanitizing common areas at the two buildings and neighboring complexes. Tenants were told that both buildings would remain open.

The wife of a person who works at the Defense Security Cooperation Agency, which is housed at 201 12th St., said the patient in question was a U.S. Marine whose diagnosis was announced by the Pentagon on Saturday. The woman asked not to be named to avoid consequences for her husband.

She said employees were told Sunday that they should stay home Monday “if they had been in contact with this gentleman, within six feet, for more than 15 minutes in the last two weeks.”

On Monday, the agency sent the remaining employees home “just for the day, while they were cleaning,” said the woman. “And then they’re having them come back in tomorrow.”

There are several factors behind a directive to self-quarantine, said Montgomery County health officer Travis Gayles. They include the type and duration of the interaction with the infected person and that person’s condition at the time of the interaction.

For example, at the post-funeral reception at the retirement community in Rockville, authorities determined that only people who had physical contact with the infected person are likely to be at risk. No residents of the retirement community have shown any symptoms of having the virus, officials said.

“These are not the same cases,” Gayles said. “You have to ask deeper questions.”

Hogan gave more details Monday on two Maryland patients whose diagnoses were announced Sunday. A Harford County woman became sick after traveling to Turkey, while a Montgomery man who fell ill was recently in Egypt and Thailand.

An additional 12 Maryland residents who have not shown symptoms are on the Grand Princess cruise ship off California, Hogan said.

The governor canceled all out-of-state travel for state workers until further notice and said agencies should be prepared for extended periods of telework.

Cole, the D.C. pastor, has been quarantined at MedStar Georgetown University Hospital in stable condition since Saturday. He first became sick after returning from a Feb. 22 conference of Episcopal leaders in Louisville.

A D.C. health official said there is “medium risk” for people who came within six feet of Cole on Feb. 24 and between Feb. 28 and March 3. Officials said people at the church on those dates should self-quarantine until 14 days after their most recent contact.

“That is when our case was symptomatic,” said Anjali Talwalkar, senior deputy director for the city’s community health administration. “So anybody who was potentially exposed during that time, out of caution and best practices for disease control, that’s the recommendation.”

Bowser said the city has leased a facility to use as a quarantine site if necessary, and she is evaluating whether she needs the power to impose quarantines by declaring a public health emergency. In the meantime, the mayor said people should take the self-quarantine message seriously.

“We don’t see it as a ‘nice to.’ It’s a ‘must to,’ ” Bowser said. “If you’ve been exposed, you need to self-quarantine, and we recognize that there will be hardships.”

The church said in a statement Monday that a “large number” of parishioners have confirmed they are quarantined; none has reported symptoms that suggest they are infected.

Tom Crocker, 70, a Georgetown resident and lifetime church member, said he is staying at home with his wife until Sunday because he attended a March 1 service. He had already stockpiled food because of the virus before learning that Cole was ill.

“I was shocked and amazed to find that our rector was the first case [in the city]. It’s one in a million that would happen,” said Crocker, a retired lawyer who was not showing symptoms.

But Jim Cannon, 67, said he has no plans to hunker down, though he recalls shaking Cole’s hand and taking Communion from him on March 1. He said he is feeling fine and would rather take advice from his doctor than the mayor. Cannon, who lives in Silver Spring, played golf Monday in Reston, keeping a club’s distance away from friends and driving alone in his cart.

“This isn’t the black plague. We are not dropping like flies,” he said. “I guess I’ve just been around too long to think we all need to go into a shelter mode.”

Several Republican members of Congress announced they would self-quarantine after interacting with a man at CPAC who was later diagnosed with the coronavirus.

But Hogan said Maryland was not issuing a quarantine order for the thousands who attended the conference at Gaylord National Resort & Convention Center because the infected man had “limited contact” with others.

The union that represents Gaylord workers said it is working with management to ensure precautions are taken to prevent the spread of the virus and employees aren’t penalized for missing work. Labor leaders are concerned about the economic impact the coronavirus outbreak could have for hospitality workers. With hotel bookings down, many are already being laid off, some union leaders said.

“We are advising our members that if they do not feel well that they should stay home and contact their health-care provider,” said John Boardman, executive secretary and treasurer of Unite Here’s D.C. affiliate, which represents about 1,000 employees.

The second D.C. coronavirus case involves a man who was treated in Maryland but developed symptoms in the city after traveling there from Nigeria. The School Without Walls closed Monday because a staff member there had close contact with that patient. But officials later said all three people who had close contact with the patient had tested negative for the virus.

D.C. International School, a charter school, also closed Monday for cleaning because a staff member was in contact with a person who went to Christ Church Georgetown. Mundo Verde, an elementary and early childhood care charter school, closed its Northwest Washington campus for cleaning, too. All three schools will reopen Tuesday.

Georgetown Day School said it will close Tuesday for a deep cleaning because it has “community members who are closely affiliated” with Christ Church of Georgetown. The school said it “does not expect this to be a long-term closure.”

The National Gallery of Art canceled two NGA Nights events, and the Environmental Film Festival canceled all screenings scheduled to start Thursday across Washington.

Maryland’s top legislative leaders introduced emergency legislation to reduce costs for testing for the virus, prohibit price gouging, improve access to telehealth, and ensure private and public workers under quarantine do not lose their jobs.

“We must all work together to make sure that every Marylander is able to access resources to protect themselves from the coronavirus,” said Senate President Bill Ferguson (D-Baltimore City), who sponsored the bill with House Speaker Adrienne A. Jones (D-Baltimore) and Sen. Clarence K. Lam (D-Howard), the Senate’s lone doctor.

The provisions of the legislation would go into effect in a state of emergency, which Maryland is currently under. Lam said the legislation enables Hogan to take actions to protect residents from the coronavirus and to ensure those who may contract the virus receive the help they need.

“We want to ensure that the Governor and Department of Health have all the tools in the toolbox to ensure the safety of Maryland residents,” Jones said in a statement. “This is a proactive step to enable the State to prevent COVID-19 from getting a larger foothold in the state.”

In Alexandria, Mayor Justin Wilson (D) said Monday the city has split its 911 call center between two sites. “In case people in one location are somehow infected, we can keep going,” Wilson said.

Erin Cox, Luz Lazo, Antonio Olivo, Renae Merle, Jenna Portnoy, Darran Simon, Perry Stein, Patricia Sullivan, Sydney Trent and Ovetta Wiggins contributed to this report.