BRUSSELS—The European Union’s top official called on the U.S. to reverse its ban on travelers from the bloc, urging the Biden administration to act within weeks to match Europe’s opening to Americans.

The comments by European Commission President Ursula von der Leyen on Wednesday signal a growing risk that U.S. travelers could once again be banned from visiting Europe because of the coronavirus pandemic.

The EU recommended in June that member states should allow nonessential travel for vaccinated and unvaccinated Americans. The final decision is for national authorities.

EU officials review the bloc’s travel access lists every two weeks. With case numbers rising in the U.S. because of the spread of the Delta variant, there is a growing possibility that unvaccinated travelers could again be banned before the end of the summer, EU diplomats said.

EU states including Germany are facing calls to ban all nonessential U.S. visitors if the Biden administration doesn’t open U.S. borders to Europeans.

EU states including Germany are facing calls to ban all nonessential U.S. visitors if the Biden administration doesn’t open U.S. borders to Europeans.

Photo: Fabian Sommer/Zuma Press

In addition, there is growing pressure from member states including Germany to ban all nonessential U.S. visitors if the Biden administration doesn’t open U.S. borders to Europeans. Each EU member state can decide whether to allow vaccinated visitors to come.

“We must solve this problem as soon as possible and we are in contact with our American friends,” Ms. Von der Leyen said. “This cannot drag on for weeks.”

The warning came as other countries tightened their rules on U.S. visitors. Israel announced on Tuesday that from Aug. 11, it would require visitors from the U.S. and several other countries to quarantine for at least seven days on entering the country, even if they are vaccinated or have recovered from Covid-19.

The EU decision to allow U.S. travelers to visit was part of a series of moves in Washington and Europe to reset relations after the tensions under the Trump administration. It came shortly after President Biden visited Brussels to talk with EU leaders.

European officials say at the time, Mr. Biden’s team said they would tackle the ban on European visitors as a priority, but weeks later there has been no change. U.S. travel restrictions also apply to visitors from Canada, China and Brazil, among other countries.

White House Press Secretary Jen Psaki said Monday that for now, the U.S. planned to keep in place existing travel restrictions because of the spread of the Delta variant.

Tourists sit at a bar in Ronda, southern Spain.

Tourists sit at a bar in Ronda, southern Spain.

Photo: jon nazca/Reuters

European officials have grown increasingly frustrated with the U.S. stance, especially as the bloc has rolled out official vaccination certificates for inoculated EU citizens. German Chancellor Angela Merkel raised the issue during her visit to Washington last month. In Brussels, officials say they are still awaiting agreement on a new date for a joint U.S.-EU working party on the travel situation to meet. The last meeting was on July 9.

Nonetheless, there is strong pressure within parts of the bloc to keep borders open for non-European visitors during the summer season. Tourism is a vital industry for countries like Greece, Italy and Spain, which were badly hit by the pandemic.

The bloc currently allows nonessential visitors from 22 external countries.

Under its rules, the EU decides which countries to include on its recommended travel list, based primarily on the comparative health situation in external countries. The bloc and its member states are also supposed to factor in whether an external country gives EU citizens reciprocal access.

While U.S. citizens were allowed to come to the EU in June despite the continued U.S. travel ban, the EU continues to recommend no access for nonessential Chinese visitors because Beijing has blocked travel by EU citizens.

Write to Laurence Norman at laurence.norman@wsj.com