The U.S. Federal Aviation Administration warned major airports to expect a hijack attempt by Iranian-trained terrorists shortly before last weekend's takeover of an Egyptair Boeing 737, according to a copy of the telexed message on file with the Greek authorities.

The message, which was routinely circulated to Athens airport, said that 400 individuals of various Middle Eastern nationalities were undergoing training in Iran in aircraft hijacking. It gave details of 176 false Algerian passports allegedly procured by the Iranian authorities for possible use by terrorists.

The commander of Athens airport, George Papadimitropoulos, said that Greek aviation authorities ordered an immediate increase in security at the airport after receiving the message from the FAA last Friday. The increased security measures did not, however, prevent the fatal hijack of the Egyptair plane on a flight from Athens to Cairo the following day.

Fifty-nine persons were killed in the 24-hour drama, which ended when Egyptian commandos stormed the plane at Malta airport on Sunday night.

The telexed message from the FAA, a copy of which was seen by this reporter, predicted that a hijacking would take place somewhere in Europe or the Middle East in late November or December. It added, however, that there was no precise information about which airports were most at risk.

In Washington, an FAA official acknowledged the message, adding: "There has clearly been in the last weeks or months an increase in terrorist activity, but we certainly did not have any specific kind of information that one could conclude pointed to this hijacking."

The Egyptian government has claimed that the takeover of the Egyptair plane was "funded and instigated" by Libya and has made no mention of any involvement by Iran.

At a press conference yesterday, Greek Foreign Minister Karolos Papoulias said he did not believe that Libya was responsible for the latest outrage. He refused to speculate about what other country might have been involved, saying that Greece did not want to get involved in "inter-Arab disputes."

The FAA telex, which was headed "possible hijacking by Iranian-trained persons," offered no evidence to support its sweeping accusations against the Tehran government. U.S. officials from President Reagan down have frequently accused the government of Ayatollah Ruhollah Khomeini of using terrorism as an instrument of state policy.

Papadimitropoulos said Athens airport receives an average of two messages a month with information about possible terrorist incidents. Other recent messages have included a warning that terrorists could be planning to use suitcase bombs against aircraft in Europe or the Middle East.

The telexed message gave the names, old numbers, and new numbers of the 176 Algerian passports allegedly at the disposal of Iranian-trained terrorists. It added that the Iranian authorities were looking for passports for a hijack operation.

Both Iranian and Libyan airlines fly in and out of Athens and have offices here. The Greek capital lies at the hub of communications routes in the Middle East.

Although Greek officials have acknowledged that the hijackers of the Egyptair flight boarded the plane in Athens, they have rejected suggestions that the arms could have been smuggled aboard here. Security at Athens airport has been tightened considerably since last June's hijacking of a TWA airliner, which had led to a decision by the Reagan administration to advise U.S. citizens against flying to Greece. That advisory later was rescinded.

Both the TWA and Egyptair flights originated in Cairo, prompting Greek officials to claim that weapons could easily have been hidden on board there. This hypothesis is being taken seriously by the International Air Transport Association, which has sent investigators to Cairo and Athens.

Papadimitropoulos cited the increased security at Athens airport following receipt of the FAA warning about an Iranian-inspired terrorist incident as one reason that it was unlikely that the arms used to hijack the Egyptair plane were smuggled aboard here.

While western officials here generally are impressed by the security measures taken by Greece since the TWA incident, particularly in the transit lounge, they are still concerned about possible flaws in the system.

In another warning, the FAA said that airport security staff should be on the lookout for imitation Samsonite suitcases capable of carrying bombs in the side pockets. It said that the bombs, which were difficult to detect mechanically, weighed about seven pounds each.

A third message on file with the Greek authorities warned of counterfeit Moroccan passports used by terrorists.