Israel renewed its search-and-destroy attacks into southern Lebanon yesterday, less than 24 hours after the State Department severely condemned its air attacks on Lebanon and called for a show of "maximum restraint" by Israel.

The State Department had no immediate specific comment yesterday about the crossing of an Israeli assault group five miles into Lebanon to blow up a house in the frontier village of Majdal Slim.

Israeli-U.S. relations were under strain on another front yesterday as the two nations continued their quarrel over the role of the United Nations in supervising the Egyptian-Israeli peace treaty in the Sinai peninsula.

At the heart of the legalistic quibbling by both sides lies a serious political disagreement over the nature and depth of the U.S. commitments given by President Carter in March to get Israel and Egypt to sign the treaty.

Also involved is a private diplomatic agreement between the United States and the Soviet Union on a plan that would deploy a few hundred unarmed United Nations Truce Organization observers in the Sinai to police the three-year phased withdrawal by Irael.

The Israeli cabinet stunned the Carter administration on Sunday by suddenly announcing that it would not accept the U.S.-Soviet plan as a substitute for the 4,000-man United Nations Emergency Force (UNEF) that Israel, Egypt and the United States had originally agreed would police the Israeli withdrawal.

The first half of the U.S. - Soviet agreement to avoid a public confrontation on the issue in the midst of the Senate debate on the strategic arms limitation treaty (SALT) unfolded on schedule yesterday.

The United States did not ask for a full U.N. Security Council session on renewal of the UNEF mandate, which expired at midnight yesterday. The Soviet Union had pledged to veto a formal extension of UNEF to police the treaty, which Moscow strongly opposes.

The Soviet Union kept its part of the bargain by applying no pressure to prevent Secretary General Kurt Waldheim from expanding and redeploying the UNTSO force in the Sinai. Waldheim announced at a press conference that UNEF would be gradually withdrawn from the Sinai and that he would make "the necessary arrangements to ensure the further functioning of UNTSO."

But the deal continued to be strongly attacked by Israel. Yehuda Blum, the Israeli ambassador to the United Nations, said at a press conference that Israel had little confidence in Waldheim, who controls UNTSO.

Blum also repeated that Israel would not accept UNTSO as a replacement for UNEF. The United States is obligated to organize a multinational alternative military force, as called for in the treaty andand its accompanying documents, he said.

But U.N. officials and Egyptian and U.S. delegates at the United Nations maintained yesterday that the UNTSO arrangement fulfilled the U.S. obligation under the treaty and that Israel now is confronted with a "take it or leave it" proposition, since U.N. observers could police the treaty from Egyptian lines without Israeli approval.

"As long as the United Nations is in the Sinai we are happy," Egypt's deputy representative Nabil Alaraby said. "This serves to fulfill the terms of the treaty."

State Department officials said the United States was continuing to talk to Israel, however, and would not attempt to force the UNTSO plan on the Jewish state.

U.N. officials said that the 112 UNTSO officers now in the Sinai would be reinforced by 200 to 500 new officers.

State Department spokesman John H. Trattner spent much of yesterday's noon briefing interpreting the treaty's language to assert that the United States were fulfilling its obligation by putting forward the UNTSO proposal. "The president's commitment" to organize a multinational force outside the United Nations "does not arise," Trattner argued in response to a spate of skeptical questions, particularly from Israeli correspondents.