The American attempt to nudge Egypt and Israel back onto the path toward a negotiated peace resumed here last night but it had the air of an empty exercise as other events combined to overshadow the formal diplomatic process.

Assistant Secretary of State Alfred Atherton, who has begun a series of meetings with Middle Eastern leaders in an effort to break the impasse that developed in the direct Egypt-Israel negotiations last month, met with Foreign Minister Mohammed Kamel to discuss possible formulations for a declaration of principles that would be the basis for a peace agreement.

Yet Kamel and other Egyptian officials are more preoccupied at the moment with the aftermath of the Larnaca airport commando raid. Atherton is scheduled to have a working lunch with Kamel and afterward will return to Jerusalem. The Americans are hoping that the Cyprus crisis will cool off and the Egyptians can again give their attention to the negotiations with Israel, informed officials said.

Kamel returned here only Wednesday from West Germany, where he was saying belated farewells after his tour as ambassador to Bonn. He spent much of the day in Ismailia with President Anwar Sadat and Prime Minister Mamdouh Salem discussing the bitter Egyptian dispute with Cyprus.

Egypt has terminated its diplomatic relations with the Nicosia government of President Sypros Kyprianou and withdrawn its recognition of him as the lawful leader of Cyprus. The Egyptians have indicated that they will take further steps against Cyprus but it is not yet known what they will be.

Legal experts at the Foreign Ministry drafted a report yesterday on the actual effects of the withdrawal of recognition -- a move that could bring this county into conflict with Greece if, as some officials here speculate. Egypt gives any form of recognition to the Turkish-sponsored regime that controls the northern third of Cyprus.

Egyptian press commentary yesterday reflected Sadat's outrage over Cypriot "treachery" in opening fire on the Egyptian commandos who were storming the commandeered Cyprus Airways jetliner in an effort to capture two gunmen who had murdered a prominent Egyptian journalist.

On paper, the entire raid was a fiasco for Egypt -- 15 commandos were killed, one of Egypt's six American-made Hercules transport planes was destroyed, and the gunmen are still in Cypriot custody.

Yet Sadat has again shown his foes that he is not a man to be trifled with. Time and again over the past two years, he has risked failure and ridicule to get what he wants to protect what he sees as Egypt's interests --and in defying Kenyan resistance to fly arms to Somalia -- and observers here see the Cyprus raid as consistent with that pattern.

Sadat has retired to his Ismailia rest house to nurse a bad cold that forced him to cancel most of his schedule, official sources said. He returned from a grueling tour of the United States and Europe to face a turbulent week that featured a minicrisis with Kenya over the seizure of an Egyptian aircraft that was flying over Kenya on its way to Somalia with a shipment of ammunition, as well as the spectacular break with Cyprus over the commando raid. He needs at least a week of rest, Egyptian officials said.

Even if Sadat were at full strength and giving the Atherton mission his full attention, however, it is unlikely that it would produce any substantive results, informed officials siad.

Neither the Israelis nor the Egyptians have changed their basic positions since Atherton was here last month, informed sources said, and the place to look for substantive developments is not in the Atherton shuttle but in the visit to the United States next month of Israeli Prime Minister Menachem Begin.

In the meantime, Atherton is seeking ways to bridge the gaps between the proposed wordings of a declaration of principles that have been offered by the Egyptians and the Israelis. It is understood that the most difficult issue remains the proposed article about the fate of the occupied territories and the Palestinians.

Egypt has said it would accept the formula offered by President Carter when he met Sadat at Aswan in early January. It calls for settlement of the Palestinian question "in all its aspects" and for granting the Palestinians the right to participate in the determination of their own future.

Israel has balked at both of these formulations and has given Atherton alternatives to discuss with the Egyptians. Official sources said that Atherton was hoping to receive from the Egyptians a precise and definitive response to the Israeli suggestions, with the understanding that the United States may be prepared, at some time in the future, to offer language of its own that it would try to persuade both sides to accept.