A man checks in at a Covid-19 testing site in the international arrivals area of Los Angeles International Airport in Los Angeles, California on December 22, 2021.A man checks in at a Covid-19 testing site in the international arrivals area of Los Angeles International Airport in Los Angeles, California on December 22, 2021.

The rule that anyone flying into the US must have a negative Covid-19 test before departure is hurting the country's tourism industry.

After the United Kingdom, Italy, Greece and others lifted requirements, the push is on.

Travelers flying into the U.S. are still required to provide proof of a negative Covid-19 test regardless of their vaccine status or citizenship. Proof that they recovered from Covid can be presented by people. Travelers are required to present a negative Covid test in other countries.

Marriott CEO Tony Capuano said in a statement to CNBC that requiring pre-departure testing creates uncertainty for travelers and may lead them to choose a destination with lessfriction. If we don't eliminate those unnecessary barriers, the US will miss out.

More than 40 U.S. mayors, including from San Francisco and Miami, sent a letter this week to the White House Covid-19. According to the letter, American cities are struggling to get international visitors.

Travel industry executives met with Jha last week, but they didn't know when the requirement would end.

After the meeting, the president of the U.S. Travel Association told CNBC that they couldn't say when pre-departure testing would be lifted.

There was no response from the White House.

Jon Bortz, CEO of the Pebblebrook Hotel Trust, said that predeparture testing is holding international travelers back from booking a trip to the U.S.

Glenn Fogel said the test requirement is pushing people to visit other countries. People just find ways around the requirement.

Fogel said that they see instances of people avoiding the restriction by flying into Canada or Mexico.

In a note to investors Wednesday, Morgan Stanley analyst Jamie Rollo wrote that the testing requirement is becoming more concerning for cruise travelers who worry about being stuck on a ship testing positive

On CNBC's "Closing Bell" Tuesday, the CEO of InterContinental Hotels Group expressed his displeasure with the country's testing requirements.

He said it was out of step with the rest of the world