A man who allegedly attempted to hijack an airliner from Ukraine is escorted by police after the plane landed in Istanbul. Agence France-Presse/Getty Images

SOCHI, Russia—Security precautions related to the Sochi Olympics tightened again as the U.S. Transportation Security Administration said it had implemented a "no liquids" policy for carry-on bags on flights from the U.S. to Russia.

The new policy comes as jitters about security at the Sochi Games surfaced again when a passenger on a Friday flight from Ukraine to Turkey allegedly declared he had a bomb and attempted to divert a flight to Sochi. After the pilot issued a distress signal, Turkey scrambled fighter jets to escort the plane safely to Istanbul, where the man was arrested. The incident played out just as the Olympic opening ceremony was about to begin in Sochi.

The TSA action follows a similar move by Russia last month. Russia put in place a no-liquids policy for flights originating within the country, a move it said was a response to potential threats against commercial aircraft. The TSA said it implemented a similar "precautionary measure" on Thursday for direct flights between the U.S. and Russia.

The alleged hijacking incident revived the security issue for Olympic organizers on Saturday. In a press briefing, the Sochi organizers played down the incident and deferred security concerns to Russian authorities.

"We were not worried about this incident. We received no threats," said Dmitry Chernyshenko, president of the Sochi 2014 organizing committee. He added that Ukrainian and Turkish authorities contacted the organizers following the attempted hijacking, but declined to say when Russian state leaders were notified.

"Totally speaking, security is an issue for the Russian authorities, so the IOC isn't really in a position to comment. It seemed like a minor incident," said Mark Adams, a spokesman for the International Olympic Committee.

Write to Bruce Orwall at bruce.orwall@wsj.com and Sara Germano at sara.germano@wsj.com