BRUSSELS — The summer started on a hopeful note. Coronavirus cases were falling, and inoculation rates were rising on both sides of the Atlantic. The European Union moved to lift its restrictions on travel from the United States, and newly vaccinated tourists eagerly embarked on their first “post-pandemic” trips.

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       But now three months later, the United States still hasn’t lifted the Trump-era rules banning most European travelers, the State Department is telling citizens to avoid 10 of the continent’s countries, and the European Union is considering shutting its doors once again to Americans, as U.S. cases soar.

       The European Union’s official recommendations stipulate that countries on its “safe list” should have recorded no more than 75 new covid-19 cases per 100,000 residents over the last 14 days. But the U.S. rates are far higher. The most recent data from the European Center for Disease Prevention and Control lists the United States at nearly 270 cases per 100,000 people. Those numbers, though, are out of date — last updated Aug. 1. They obscure the worst of the most recent surge. The current number is closer to 400, or more than five times the E.U. threshold, according to a Washington Post tally.

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       On Monday, after rumors circulated that the European Union would reimpose restrictions on U.S. travelers, the bloc decided against it, for now, allowing Americans to continue flocking to European cities and beaches, which have been desperate to revive tourism-starved economies.

       But the 27-member club also signaled that policy could soon change. The Council of the European Union, the body through which member states coordinate policy, said it would continue monitoring the countries, including the United States, where “the covid situation has deteriorated,” an official told The Post.

       If the picture does not improve in the next two weeks, the council may remove the United States from the safe list, said the official, speaking on the condition of anonymity because they were not authorized to discuss the matter publicly.

       That could mean a ban on unvaccinated travelers. E.U. members could also impose what they have called an “emergency break,” which would halt travel regardless of vaccination status.

       The possibility of a review looms as U.S. authorities are urging Americans to avoid much of western Europe. On Monday, the State Department issued “Do Not Travel” advisories for France and Iceland, citing the virus levels in those countries, which are similar to U.S. rates. Officials had already attached that highest-level warning to Britain, Cyprus, Greece, Ireland, Malta, the Netherlands, Portugal and Spain.

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       And, despite an E.U. vaccination campaign that has surpassed America’s, the United States has maintained its rules barring entry to most European travelers. President Donald Trump first imposed the ban at the beginning of the pandemic. It applies to residents of Britain, Ireland and Europe’s 26-country, border-free Schengen zone.

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       The White House has directed questions on the ban to its public health experts. Spokesmen at the Centers for Disease Control and Prevention, which maintains the list of banned countries, did not respond to a request for comment on the restrictions or when they would be lifted.

       “I certainly understand there’s a desire to do that by many people in the United States, many people around the world,” White House press secretary Jen Psaki said at a briefing last week. “We understand that. I just don’t have an update on it and when that will happen.”

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       The persistent restrictions have exasperated many in Europe. Critics of the U.S. policy say it’s hurting businesses, dividing families and makes little epidemiological sense, as infection levels in the United States are far higher than in most E.U. countries.

       “We insist that there are comparable rules for travelers in both directions,” Ursula von der Leyen, president of the European Commission, said in an interview with the German outlet RND last week. “We have to solve the problem as soon as possible, and we are in contact with our American friends. This must not drag on for weeks longer.”

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       European Commission spokesman Adalbert Jahnz said at a Tuesday news conference that talks with the United States were ongoing.

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       “We consider there is a good case for the U.S. to remove their travel restrictions, or at least adapt them, given the improving health situation in the E.U. overall,” he said.

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       A recent column in the conservative German newspaper Die Welt compared the U.S. policy to a “humiliation.” As a result, the paper’s correspondent wrote, many Europeans would probably embrace new restrictions on Americans, but “unfortunately nobody would benefit from it.” European countries, especially those around the Mediterranean, need the tourism dollars to survive, he argued.

       In France, for instance, tourism accounted for more than 7 percent of the country’s gross domestic product before the pandemic. The economies of Italy and Greece are even more dependent on the sector, with tourism accounting for 13 and over 20 percent of their GDPs, respectively.

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       The return of U.S. tourists to Greece excited the sector this year, when nationals from many other countries were still restricted from traveling there. The U.S. ambassador to Greece, Geoffrey R. Pyatt, called 2021 “the year of American tourism in Greece.”

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       The E.U. official said the council’s decision this week not to reinstate restrictions on the United States was based on consultation with public health officials and the European Commission, the bloc’s executive branch.

       The rules are not legally binding. If southern European countries wanted to preserve their longer summer tourism season, they could, just as Greece opened to U.S. tourists earlier than its neighbors did. But the E.U. guidance sets an important precedent because borders are open between member states, and there’s an interest in maintaining a united stance.

       Representatives of the tourism industry said the European Union’s hesitancy to reimpose travel restrictions on Americans now may reflect a growing awareness of the potential economic fallout from such measures.

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       “Traveling and mobility is fundamental for the European Union economy,” said Luís Araújo, the president of the European Travel Commission, an organization that seeks to promote travel to the European Union.

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       According to the organization, U.S. arrivals to Europe declined by more than 80 percent last year, compared with 2019. Italy, France and Spain are among the European countries that are most dependent on U.S. travelers, but other nations were seeing a rising interest before the pandemic.

       Any sudden change in regulations negatively affects trust in the tourism sector, Araújo said, and the European Union may be increasingly wary of taking action that could damage the industry.

       “It’s crucial,” Araújo said, “to give some confidence back to the sector.”

       Noack reported from Paris.