Having failed to win over the Carter administration to its views on a Middle East peace treaty, Israel's new strategy appears to be to try to reestablish direct talks with Egypt.

Reports in the Israeli press yesterday said Defense Minister Ezer Weizman would go to Cairo soon to resume talks, but Weizman told reporters later that there were no immediate plans for such a trip.

Nonetheless, when Prime Minister Menachem Begin answers Egyptian President Anwar Sadat's latest letter this week, it is expected that Begin will make overtures toward resumption of the talks, which Sadat broke off in January.

The Israeli Cabinet on Sunday unanimously endorsed the hard-line position Begin took in his talks with Carter. This and the expressed willingness of his biggest coalition partner to let Begin attempt to resume talks with Egypt appear to have eased, for now, the severe domestic political pressures Begin had been under.

Transport Minister Meir Amit of the Democratic Movement for Change, a coalition partner of Begin's Likud Party, said yesterday that his faction wants to give Begin a chance to resume negotiations with Egypt even though the Democratic Movement does not agree with all the positions Begin took during his talks in Washington.

Even before it failed to win Carter administration support for its positions, Israel had expressed dissatisfaction with U.S. mediation efforts, especially the shuttle diplomacy of roving U.S. Ambassador Alfred Atherton.

Weizman, in a recent interview with the Israeli daily Maariv, said:

"We have to enter into renewed discussions with Egypt. That is the way, not American mediation. Atherton's mediation mission was of no benefit either to ourselves or to the Egyptians. It may even have caused damage and delayed the peace process."

Foreign Ministry officials have hinted that the coming trip of Foreign Minister Moshe Dayan to Romania may be connected with the efforts to renew negotiations with the Egyptians.

Romania is the only Communist country that has diplomatic relations with Israel, and it played a role in the preliminary maneuvers that led to Sadat's visit to Jerusalem in November.

Meanwhile, Ashraf Ghorbal, the Egyptian ambassador to the United States, arrived in Cairo yesterday with a message from President Carter for Sadat.

Ghorbal gave no details on the contents of the message but it reportedly deals with Carter's view of his unsuccessful talks with Begin.