The crisis in Greek-U.S. relations caused by the hijacking of a Trans World Airlines plane after takeoff from Athens Airport in June has been eased considerably with the Greek government's prompt improvement of its airport security, according to U.S. and Greek officials here.

These officials said both governments are now actively seeking to put the incident behind them and that both had given every indication they are determined to see relations improve.

"It is true the TWA incident harmed our relationship and there is still a taste of bitterness," said one senior Greek Foreign Ministry official who spoke on the condition that he not be named. "But there is a strong will from both sides to improve relations and I think there is evidence that they have improved substantially of late."

The U.S. government had expressed displeasure at the fact that two of the Shiite Moslem hijackers boarded the TWA Cairo-to-Rome flight during a stopover in Athens and that an accomplice captured by the Greeks at the airport promptly was freed in exchange for the release of Greek hostages on the airplane.

The Reagan administration, never very sympathetic to the foreign policy of Prime Minister Andreas Papandreou, a Socialist, promptly accused Greece of being lax on terrorists within its borders, failing to provide adequate security at its international airport, and giving in to terrorist demands. As a result the Reagan administration asked U.S. airlines to boycott the Athens airport and warned American tourists that traveling through the airport could be dangerous -- two measures that hit directly at Greece's lucrative tourist business at the height of the summer season.

The Greek government's initial reaction was that it was being unjustifiably singled out for punishment even though it had never been established whether the hijackers' weapons were put on the plane in Athens or had been smuggled aboard in Cairo, where the flight originated.

The result of the dispute, Greek and U.S. officials seem to agree, was to plunge the often delicate U.S.-Greek relationship to its lowest point in more than a decade.

Despite its public anger and protest, however, the Papandreou government moved quickly to improve security at the airport, responding to all recommendations made by U.S. Federal Aviation Administration officials and the International Air Transport Association.

Greek officials said the security staff at the airport had been increased from 400 to 700 people, baggage X-rays had been stepped up and improved, and monitoring of passengers had been expanded. Plans have also been made to build a $250,000 fence with guard towers around the vulnerable airport, which sits in a densely populated suburb of the Greek capital.

As a result of the Greek action, U.S. flights were interrupted only briefly.Last week, after FAA inspectors checked the security improvements at the airport, the U.S. travel advisory was canceled. The promptness of Greece's action, U.S. officials here said, was a sure sign that Athens wanted an improvement in relations. Greek Foreign Ministry officials, meanwhile, point to the U.S. lifting of the travel advisory as evidence that Washington also seeks an improvement.

The six-week crisis, however, damaged Greece's already ailing economy. According to Nikos Skoulas, secretary general of the state-run National Tourist Organization, the U.S. travel warning led at least 12,000 American tourists to cancel visits to Greece, and there are fears that the total could prove twice that high when the full figures are in.

"That means $40 million in lost income," Skoulos said in a news conference this week, shortly after returning from a visit to the United States to tell travel agents that Greece was safe for tourists despite the TWA hijacking.

"Mr. Reagan said he issued the travel advisory for security and I have to believe him, but we feel we were treated unfairly," Skoulos said. "What's lost is lost. Now we have to think about the future."