The United States warned Americans yesterday that they risk "potential danger of terrorist acts" if they use the airport in Athens, Greece.

The advisory is highly unusual when applied to an airport or country not in a war zone and is part of an escalating U.S. and international effort to persuade the Greek government to improve security at that airport, where the hijacking of Trans World Airlines Flight 847 began Friday.

The ultimate U.S. action would be to prohibit Olympic Airways, the Greek airline, from flying to the United States and to ban TWA and Pan American World Airways from serving Athens.

In his televised news conference last night, President Reagan said he has asked that "all U.S. carriers review the wisdom of continuing any flights into Athens until the security situation there improves."

Reagan said he has asked Secretary of State George P. Shultz and Secretary of Transportation Elizabeth Hanford Dole to consider "whether we should terminate the service of foreign air carriers whose governments do not honor appropriate international conventions or provide adequate security at their airports."

Besides ordering the travel advisory, Reagan said he has asked Dole and Shultz to "explore immediately an expansion of our armed sky marshal program aboard international flights." Dole, in a statement issued last night, said she and Shultz are coordinating a study of air-travel security.

"I think you're going to see further action because a lot of countries besides the United States have been unhappy with that airport," a State Department source said.

Passenger and baggage screening at Athens is so inadequate that individual airlines have established their own such systems, and the airport perimeter is easily breached, according to several sources.

"We have decided to issue a travel advisory warning American citizens of the potential danger of air travel to, through or from Athens," State Department spokesman Bernard Kalb said.

"We have repeatedly made our concerns known to the Greek government in the past, and a U.S. airport security team visited Athens in February.

"Although the Greek government has expressed its willingess to improve conditions at the Athens airport, specific steps have not been taken yet, and security there is still inadequate. We have no choice but to warn our citizens of the potential danger of terrorist acts there," he said.

Kalb said, "U.S. citizens and aircraft can use the airport at Athens at their discretion. However, the United States is acting to advise them of the previous terrorist problem and the potential for additional incidents in the future."

His statement did not refer to the hijacking.

Rodney Wallis, security director for the International Air Transport Association (IATA), the Montreal-based group that represents international airlines, said, "All we can do at this stage is raise the level of pressure on the Greek government . . . to make the Greek authorities realize the seriousness of the situation.

"On this occasion, an American citizen has been killed and, for all we know, a similar fate could be awaiting the other hostages. The Greeks have to understand that their laissez-faire attitude is unacceptable . . . . There is no reason why a legitimately elected democratic government can't provide a secure airport."

Wallis said an IATA security-inspection team, including a Federal Aviation Administration representative, visited Athens just before the hijacking last week. It sought Greek government recision of an order that would, in effect, make it impossible after June 30 for individual airlines to screen passengers and carry-on baggage, he said.

Wallis said he is awaiting the Greek response on that issue and on a request that his IATA team make a full airport-security survey next week.

He said he also wants to learn the results of any Greek investigations of the hijacking. "One of the things we need to ascertain is what route the weapons took to get on the plane," Wallis said.

Echoing U.S. officials, Wallis said "it would be surprising" if the guns and hand grenades used by the hijackers had slipped through the TWA security net by being wrapped in Fiberglas, as one of the hijackers has claimed.

Reagan urged last night that U.S. allies "redouble their efforts to improve airport security" and "take steps to prevent travel to places where lawlessness is rampant . . . ." He called on Americans not to enter "any Middle Eastern country that does not publicly condemn" the hijacking.