President Trump said Monday that Americans should avoid gathering in groups of more than 10 people, eating in restaurants or taking nonessential trips, his most significant push yet to combat a viral outbreak that has rocked financial markets and disrupted the daily lives of Americans.

Taken together, the guidelines were the closest the federal government has come to calling for a nationwide quarantine, with the White House arguing that the United States has just 15 days to halt the spread of the coronavirus.

A day after giving a self-congratulatory news conference in which he declared the U.S. government had “tremendous control” over the pandemic, Trump on Monday appeared chastened by the magnitude of the crisis facing the nation and testing his presidency.

“If you’re talking about the virus, that’s not under control any place in the world,” he said Monday, describing the virus as “an invisible enemy” and “a very bad one” that could continue to afflict the United States until August or later.

As Trump spoke, stocks continued their historic plunge, with the Dow Jones industrial average ending the day down almost 13 percent, falling almost 3,000 points for its worst daily slide since 1987.

Several state governors on Monday voiced frustration with Trump’s handling of the crisis, taking unilateral steps to protect their residents as they criticized the lack of clarity and direction from Washington.

Ohio Gov. Mike DeWine (R) moved to postpone that state’s primary election, scheduled for Tuesday, until June. The governors of New York, New Jersey and Connecticut issued joint directives closing bars, gyms, movie theaters, casinos and dine-in restaurants.

San Francisco Mayor London Breed on Monday ordered all residents to stay indoors, except for essential needs, part of a regionwide call for 6 million residents in the Bay Area to largely remain in their homes except for grocery shopping, dog-walking and emergencies. The leaders of six Bay Area counties, among the hardest hit by the widening coronavirus, jointly implemented the order, which is one of the nation’s strictest containment and social-distancing efforts. It is set to remain in place through April 7.

Those and other officials around the country said they were taking unprecedented steps to combat the spread of covid-19, the disease caused by the virus. There are now more than 4,300 confirmed cases throughout the country, and more than 80 have died, including 48 in Washington state and 10 in New York. Globally, the virus already has killed more than 7,100 people, and an accelerating contagion is taking hold in places such as Italy and Iran.

Canadian Prime Minister Justin Trudeau announced Monday that Canada would shut its borders to almost all noncitizens, part of travel restrictions that have been implemented across the globe. German Chancellor Angela Merkel on Monday announced a nationwide shutdown of bars, nightclubs, theaters, museums, brothels, casinos, cinemas, swimming pools and gyms. Religious services also were banned.

The United States is just beginning to ramp up its testing capacity, something the Trump administration has acknowledged was a shortcoming in its early response. After struggling to ensure that widespread tests would be available for people with symptoms, the Trump administration said Monday that it had confirmed 1 million tests had been deployed nationwide, with plans to scale that up in coming weeks. State and local officials began to roll out additional test sites Monday, including drive-through testing in parts of New York state.

The lack of adequate testing has been a key challenge in stopping the spread of the coronavirus globally, according to World Health Organization Director General Tedros Adhanom Ghebreyesus.

During a news conference on Monday, he urged country leaders to increase their testing and isolation methods to truly make a difference.

“You cannot fight a fire blindfolded, and we cannot stop this pandemic if we don’t know who is infected,” he said, emphasizing the need to break chains of transmission. “We have a simple message for all countries: test, test, test.”

The Trump administration also faced questions from state officials about how prepared the federal government is to lead a surge in hospital capabilities and equipment in advance of an expected increase in coronavirus patients.

Trump said during a conference call with the nation’s governors on Monday morning that states should not rely on federal officials to provide respirators, ventilators and other medical equipment. Instead, the states should try to work on obtaining the equipment on their own, Trump said, a comment that was met with backlash from some state governors who accused Trump of shirking his leadership responsibilities.

Trump tweeted Monday afternoon that he “just had a very good teleconference with the Nations’s Governors” and that it “went very well.” But he singled out one particular state executive, calling on New York Gov. Andrew M. Cuomo (D) to “do more.”

Cuomo shot back via Twitter: “I have to do more? No — YOU have to do something! You’re supposed to be the President.”

Trump and his coronavirus task force also recommended that states with evidence of community transmission of the virus should shut down schools, as well as bars, restaurants, gyms and other gathering spots. The administration also recommended that the elderly and people with serious health conditions stay at home and that nursing homes should halt all social visits. Thus far, the elderly and infirm have been more susceptible to the virus.

“It isn’t an overreaction,” Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, said of the recommendations released Monday.

Officials warned that the outbreak could go on for months, though Fauci said that the guidelines were only meant to be operative for 15 days.

Trump said it is possible the economy will go into recession, while predicting that the economic slowdown would be reversed once the pandemic ends.

But the far-reaching impact of the outbreak already has begun to leave an indelible mark on the nation’s institutions, including its schools.

From Washington state to Pennsylvania, school closures affected an estimated 32.5 million public school students in at least 64,000 schools, according to a tally kept by Education Week.

On Monday, the National Education Association recommended shutting down all schools nationwide for two weeks, an unprecedented move that the group said reflected the scope of the crisis.

The Centers for Disease Control and Prevention has “recommended banning all gatherings of more than 50 people, but exempted schools,” NEA President Lily Eskelsen García said in a statement. “We are calling on the CDC to update their guidance and include schools for the safety of everyone.”

The two-week timeline reflected what public health officials say is a critical period that could determine how widespread the virus becomes, and how many people ultimately will die of it. The Trump administration has significantly expanded and increased the scope of its social distancing recommendations in recent days as it has watched alarming figures released by Italy, where hundreds of people have been dying daily from the outbreak.

U.S. surgeon general Jerome M. Adams said the United States is at “a critical inflection point” when it comes to the coronavirus outbreak, with current numbers tracking closely with where Italy was two weeks ago.

“We have a choice to make as a nation: Do we want to go the direction of South Korea and really be aggressive and lower our mortality rates, or do we want to go the direction of Italy?” Adams said during a Monday morning appearance on “Fox and Friends.” “When you look at the projections, there’s every chance that we could be Italy.”

Italy is experiencing the worst outbreak outside of China. Italy’s nearly 25,000 confirmed cases are forcing health officials to ration care. More than 2,100 people have died.

Trump, who had previously downplayed the virus, said new government modeling — which takes into account Italy’s experience — led to his more aggressive stance.

“We’ve made the decision to further toughen the guidelines and blunt the infection now,” Trump said during the briefing. “We’d much rather be ahead of the curve than behind it.”

Efforts to blunt the economic impact of the crisis also ramped up Monday as the stock market’s plunge made clear the threat coronavirus posed to the global economy.

Trump announced that the federal government would be “backstopping” the airline industry, which has suffered amid a drop-off in demand for travel.

“We have to back the airlines,” he said. “It’s not their fault.”

While it was not clear what kind of proposal Trump had in mind, airlines offered a few ideas Monday, asking for more than $50 billion in federal assistance.

The aid would come in the form of tax relief, loans and other financial aid, including nearly $30 billion in grants for passenger airlines and cargo carriers, according to a document from Airlines for America, the industry’s leading trade group.

“This is a today problem, not a tomorrow problem,” said Nicholas E. Calio, president and chief executive of Airline for America. “It requires urgent action.”

Senate Minority Leader Charles E. Schumer (D-N.Y.) used similar language as he announced plans for a new aid package of at least $750 billion aimed at boosting hospital capacity and providing direct financial support to Americans.

“We will need big, bold, urgent federal action to deal with this crisis,” Schumer said Monday, previewing a package that he planned to unveil Tuesday.

Sen. Mitt Romney (R-Utah) called on the federal government to immediately provide a $1,000 check to every American adult, saying Monday that such action was warranted to blunt the economic hardship caused by the coronavirus.

For his part, Trump has called for a payroll tax cut lasting through the end of the year, a move that would lower taxes for Americans just as they face the choice of whether to reelect him.

On Monday, it was not clear which relief proposal would gain traction in a divided Congress, though the pandemic has increased the likelihood of major bipartisan legislation in an election year.

While Trump said a recession was a possibility, he predicted that a pent-up demand would be unleashed once the pandemic subsided.

“Once this virus is gone,” he said, “I think you’re going to have a stock market like nobody’s ever seen before.”

Wilson reported from Santa Barbara, Calif. Robert Barnes, Brent Soloway, Lateshia Beachum, Kim Bellware, Lori Aratani and Gregory S. Schneider contributed to this report.