“The restriction stops people not goods,” Mr. Trump later tweeted.

Hours after the address, the State Department advised U.S. citizens against all travel abroad, even to countries not yet experiencing an outbreak. The department warned of mandatory quarantines, travel restrictions and other measures that could complicate international travel.

The virus has spread to more than 100 countries, roiled markets and disrupted daily life across the country and around the world. The sober address marked Mr. Trump’s most direct response to date, though he again tried to sound an optimistic note and defended actions already taken by his administration.

“This is not a financial crisis,” Mr. Trump said. “This is just a temporary moment in time that we will overcome as a nation, and as a world.” U.S. stock futures and global stock markets dropped after the president announced the new travel restrictions.

The restrictions are sure to hurt the airline industry, already suffering from a plunge in travel as the virus has taken hold, and are likely be a major blow to Europe’s economy.

The Department of Homeland Security on Wednesday night said a proclamation signed by the president applies to most foreign nationals who have been in any of 26 European countries during the 14 days before their scheduled U.S. arrival.

The ban applies to the countries in the Schengen Area, a zone without border controls, where foreigners from outside Europe can travel freely. The U.K. isn’t inside the Schengen Area—and wasn’t even before it exited the European Union—though the country hasn’t escaped coronavirus.

U.S. citizens and green-card holders are exempted from the temporary ban, as are their spouses and children. Citizens and green-card holders under the age of 21 are also eligible to bring parents into the U.S. Passengers on flights that take off Friday before midnight will still be eligible to enter the U.S., even if they land after the ban takes effect.

Europe is the largest regional destination for U.S. travelers, according to U.S. Transportation Department, with 72.4 million passengers in the year ended June 2019. Central America is second, with 43.2 million passengers in the same period.

Airlines scrambled to understand what Mr. Trump’s announcement would mean for their operations. Carriers have already announced cuts to flying capacity all over the world due to flagging demand, but had planned to continue some flights to and from Europe.

“We are in contact with the federal government to understand and comply with this directive. The health and safety of our customers and team members remains our highest priority,” American Airlines Group Inc. said in a statement. American said the directive would affect 14 flights a day from Paris, Frankfurt, Munich, Barcelona, Madrid and Zurich.

“Delta has and will continue to quickly make adjustments to service, as needed, in response to government travel directives,” Delta Air Lines Inc. said in a statement. A spokesman for United Airlines Holdings Inc. said the airline would comply with the announcement.

Mr. Trump, who spoke for about 10 minutes, also said he would take emergency action “to ensure that working Americans impacted by the virus can stay home without fear of financial hardship.” He said any aid would be targeted for workers who are ill, quarantined or caring for others. The administration also plans to ask Congress to extend additional relief to those workers, he added.

Last year, 24% of U.S. workers, or about 33.6 million people, didn’t receive paid sick leave from their employer, the Labor Department said. They are concentrated in lower-wage and front-line service-sector positions. Of the lowest 10% of wage earners, only 31% had sick leave, compared with 94% of the top 10%.

Mr. Trump also said he would instruct the Internal Revenue Service to push back the April 15 tax-payment deadline for certain individuals and businesses, providing a cash cushion at a time when the economy may falter. He said the action would provide an additional $200 billion of liquidity to the economy.

Effective immediately, Mr. Trump said the Small Business Administration would offer low-interest loans to help small businesses overcome temporary economic disruptions caused by the virus. He said the administration planned to ask Congress to authorize an additional $50 billion for the program.

The president again urged Congress to approve “immediate payroll-tax relief.”

“Hopefully, they will consider this very strongly,” Mr. Trump said. The proposed payroll-tax cut faces resistance from both Democrats and Republicans on Capitol Hill.

Late Wednesday, House Democrats prepared and released an economic package that includes paid sick leave for people affected by the coronavirus and expanded unemployment insurance, reflecting priorities laid out by House Speaker Nancy Pelosi (D., Calif.) and Senate Minority Leader Chuck Schumer (D., N.Y.) at the start of the week.

Democratic lawmakers plan to pass it on the floor Thursday, though it is unclear how much Republican support it will have.

Mr. Trump said insurers had agreed to waive copayments for coronavirus treatment. But America’s Health Insurance Plans, a trade group for the industry, pointed to a press conference Tuesday where Vice President Mike Pence said insurers had agreed only to waive copayments for coronavirus testing.

Mr. Trump faces not only a national health problem but a political test as he heads deeper into the re-election campaign. A strong economy has been one of his biggest selling points, and the crisis has already taken a toll. His chief rival, former Vice President Joe Biden, is set to give a speech on coronavirus Thursday in Wilmington, Del.

The White House said that “out of an abundance of caution from the coronavirus outbreak,” the president canceled travel for events in Colorado and Nevada that were to begin Thursday.

Administration officials have previously signaled that more travel restrictions were under consideration.

During a White House meeting with banking executives earlier in the day, the president raised concerns about the spread of the novel coronavirus in Europe, according to people familiar with the matter. He called it a hotbed of the virus and said one reason for its rapid spread there is the ease with which travelers can cross borders, the people said.

Italy, suffering the largest outbreak outside of China, has imposed a countrywide quarantine and halted most commercial activity. German Chancellor Angela Merkel predicted that 60% to 70% of the country’s population could become infected with the virus, citing expert estimates.

The Trump administration first restricted travel Jan. 31, blocking U.S. entry by foreign citizens who had traveled anywhere in China in the previous two weeks and ordering the quarantine of Americans who visited the area of China hardest hit by the virus—the first such action in the U.S. ordered by the federal government in roughly 50 years.

A month later, the U.S. said it would bar entry to foreign nationals who had traveled to Iran, and issued advisories strongly urging people against travel from the U.S. to areas in Italy and South Korea.

The president has faced criticism that he has played down the threat for weeks, offering a mixed message as members of his administration have taken an increasingly sober outlook. On Twitter, Mr. Trump blasted Democrats and the news media and said it was a time for unity.

“We have a common enemy, actually, an enemy of the World, the CoronaVirus,” he wrote. “We must beat it as quickly and safely as possible. There is nothing more important to me than the life & safety of the United States!”