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The rise in Washington-area coronavirus cases continued to accelerate Tuesday as leaders scrambled to prepare for an even greater surge, cobbling together bed space and supplies while calling for more help and coordination from the federal government.

A day after leaders in the District, Maryland and Virginia ordered residents to stay home to limit the spread of the virus, the greater capital region added 477 known coronavirus cases, bringing the regional tally to 3,411.

Maryland Gov. Larry Hogan (R) described as “just not true” President Trump’s claim that getting access to testing is no longer a problem and said states are “flying blind,” without enough data to assess the true scope of the U.S. outbreak.

Virginia reported 230 new infections and Maryland 247 — each number a one-day record for its state; the District did not report new overall coronavirus cases Tuesday because it is shifting the release of data from evenings to mornings. But it announced 12 new cases among D.C. first-responders.

Six more fatalities were announced in Maryland, including the deaths of three residents of a nursing home in Carroll County that has seen a major outbreak. Virginia reported that four more people in the state had died of covid-19, the disease caused by the coronavirus. That brings the total of known covid-19 fatalities in the greater Washington area to 63.

But there also was good news. Maryland reported that 53 covid-19 patients had been released from isolation by Tuesday afternoon. The District reported that 121 of 405 covid-19 patients had recovered as of Monday evening.

Virginia has not compiled recovery data.

Maryland and Virginia have significantly ramped up testing in recent weeks, which is one reason for the surge in the number of new cases. In Maryland, more than 16,500 tests have been conducted, about 90 percent of which have been negative. In Virginia, 13,400 tests have been administered, about 91 percent of which have been negative.

The District had reported its most new cases in a single day — 94 — on Monday, and the most new test results received, 674. It has reported nine fatalities.

With health-care providers struggling to keep up, D.C. officials said Tuesday that they would start shipping personal protective equipment to city hospitals, long-term-care facilities and doctors. Assistant City Administrator Jay Melder said the city planned to release 70 percent of its stock of equipment, including hand sanitizer, more than 18,000 gloves and more than 300,000 masks. First responders and essential D.C. government agencies are also eligible to receive supplies.

Baltimore-based athletic-wear company Under Armour said it is manufacturing masks, face shields and fanny packs for nearly 28,000 health-care workers at the University of Maryland Medical System.

The medical system, which has 13 hospitals statewide, has “a baseline supply of personal protective equipment,” also known as PPE, but will need more in coming weeks and months, spokesman Michael Schwartzberg said in a statement.

Bob Atlas, president of the Maryland Hospital Association, said leaders at Maryland’s four dozen hospitals are “very concerned” about supplies to shield front-line workers.

“Trying to predict right now is an imperfect science,” Johns Hopkins epidemiologist Aaron Milstone said. “Patients are still coming in faster than they are going home. If the number of new patients stops or slows, we are in good shape. If it sustains for weeks or increases, it is going to test the system.”

One of the biggest outbreaks in the state so far is at the Pleasant View Nursing Home in Carroll County. Seventy-seven of the 95 residents at the facility have tested positive, and five people have died, including two men in their 70s and a woman in her 60s whose deaths were announced Tuesday.

The National Guard has deployed a medic unit to the nursing home to help with screening, and a county physician is also on-site to treat patients, the Carroll County Health Department said in a statement Tuesday. The 18 residents who tested negative are being cared for in a separate part of the facility.

“As tragic as it is, it’s not an unusual situation,” Hogan said in a C-SPAN interview. “It’s sort of happening in other places around the country.”

To boost bed space in Northern Virginia, the U.S. Army Corps of Engineers has identified three possible sites for temporary hospital facilities, according to a briefing Tuesday from Prince William County Executive Christopher Martino. They are: the National Conference Center in Loudoun County (capacity 1,000 beds), the Dulles Expo Center in Fairfax County (capacity 500 beds) and an unnamed facility at George Mason University in Fairfax City (capacity 500 beds).

Maryland and Virginia officials said they are consulting various computer models to get a sense of when the outbreak might peak. D.C. Mayor Muriel E. Bowser (D) said the city will release a projection this week.

To help with the rising load, George Washington University Hospital in the District said it is preparing to to offer drive-through coronavirus testing on its Foggy Bottom campus for D.C. residents who have test referrals from their health-care providers.

Hogan told NPR’s “Morning Edition” that the president’s optimistic take on testing — Trump said that he had not heard about problems with testing in weeks and claimed that the United States had tested more people than any other country — was “aspirational.” None of the testing advancements Trump touted in a conference call with governors Monday have been deployed, Hogan said.

The governor said he thinks the White House coronavirus team that includes Vice President Pence and Deborah Birx, the response coordinator, is working with facts, and “we’re listening to the team, the smart team.”

During a separate appearance on CNN’s “New Day,” Hogan, who is chairman of the National Governors Association, said governors were pushing the federal government to coordinate the purchase of scarce coronavirus supplies to avoid a bidding contest among states. Virginia Gov. Ralph Northam (D) has made the same appeal, arguing that the free-market system doesn’t work in an emergency such as this because it drives up prices.

Hogan also signed an emergency order giving Maryland taxpayers until July 15 to file their state income tax and personal property tax returns. Officials in the District and Virginia have not taken similar actions.

The stay-at-home orders issued by Hogan, Northam and Bowser got a boost from the top elected officials of 21 local governments in the national capital region, who issued a letter saying they “are joining in one voice to implore each of the more than five and a half million individuals in our region to stay home” unless performing an essential activity as permitted by authorities.

“This is the most important thing each of us can do to stop the spread of covid-19,” the mayors, board chairs and commissioners wrote in a news release. “We must be united as one region while we each do our part to protect ourselves and each other.”

Hogan called the stay-at-home order one of “the last tools” in his arsenal and said he ordered people to stay home partly because epidemiologists and other scientists said the surge in Maryland’s case count resembles what happened two weeks ago in New York, now the center of the country’s coronavirus outbreak.

Bowser said she does not expect the city to levy criminal penalties for violations of her stay-at-home order, which allows the city to jail people for up to 90 days or fine them up to $5,000.

“We expect the people of the District of Columbia to comply,” the mayor said at a news conference. “We do, of course, have penalties at our disposal, but I don’t expect we will have to use them. That’s certainly my hope.”

Residents are allowed to leave home for essential business and errands and to exercise outdoors, as long as they keep distance from others outside their household and avoid team sports.

School safety officers have been redeployed to parks, playgrounds and recreation centers while school buildings are closed this month, Bowser said. On Tuesday afternoon, the city closed outdoor basketball courts and athletic fields.

The mayor said police officers have been provided a script for enforcing the stay-at-home order, with instructions to use reminders instead of handcuffs. “Attention, everyone: We are currently in a public health emergency,” an officer says in a sample video released by Bowser. “Your gathering puts both you and others at unnecessary risk.”

Laura Vozzella, Antonio Olivo, Fenit Nirappil, Patricia Sullivan, Kyle Swenson, Ovetta Wiggins and Peter Hermann contributed to this report.