Egypt has come through the period of Israeli invasion of southern Lebanon with renewed determination to press ahead with the quest for a negotiated Middle East peace settlement.

President Anwar Sadat, who proudly boasts that he always means what he says, stressed to several audiences last week that there will be "no going back" on what he calls his "historic mission." There is every indication that this is more than public posturing: It represents a policy to which Sadat and his senior staff are fully committed.

In contrast to the furor in Israel and the doubt and uncertainty in Syria, an odd serenity prevails here over Egypt's chosen course.

The peace negotiations themselves are at an impasse, and Egypt has been sharply criticized by Arab opponents who argue that the only result of Sadat's initiative has been more Israeli occupation of Arab land.

Nevertheless, the Egyptians say, with apparent conviction, that the conflict in Lebanon proved that peace is not only desirable but necessary and that it has again demonstrated that peace cannot be achieved without a settlement of the Palestinian question.

Israel's defense minister, Ezer Weizman, is expected to return here soon for another attempt to resume the direct Israeli-Egyptian negotiations.

According to authoritiative Egyptian officials, Weizman will be received on the same terms as on his last visit March 30 - that is, the Egyptians are determined to maintain their direct communication channel with Israel and not to expose themselves to the charge that they are refusing to negotiate. Yet, unless Weizman brings what are called here "new ideas," there will be no resumption of the formal peace talks.

"We are not going to fall into the Israeli trap of having negotiations for their own sake while they keep sticking to all their old positions," a senior Egyptian Foreign Ministry official said. "There has to be something new. We dont' want to allow the Israelis to say that since they are negotiating directly with us, the Americans should stay out of it. But at the same time we have to keep the door open."

No date has been set for Weizman's next visit. The Cairo press has been predicting intensive new rounds of diplomatic activity, possibly involving some new American proposals, in the coming week or so but high-ranking Egyptian sources say they are not expecting any major new moves until the Israelis settle their own internal disputes over negotiating policy.

The Egyptians admit they had doubts about receiving Weizman last month in the midst of the Israeli invasion of Lebanon. But they say that by allowing him to come they remove any lingering doubt about their sincerity or determination to press for peace, while their refusal to reopen formal negotiations buttressed their credibility as tough negotiators determined not to surrender.

"A lot of people, especially the other Arabs, felt that when the Israelis invaded, that was the end of the peace process," a senior official said. "But we felt we couldn't quit now. We have too much invested in it, and the expectations of the people would be let down.We've only been at it a few months and there's no sense losing everything to impatience."

Sadat told an international symposium of journalists last week that "I shall never let the hundreds of millions all over the world down at all. I shall be doing my best and I shall continue with perseverance until the mission is completed."

he acknowledged that Egypt and Israel are still speaking "two different images" about the terms for peace. But based on Sadat's public comments and the private assessments offered by Egyptian officials, it is clear that the Egyptians think it is Israel, not Egypt, that is under pressure to say something new. In the Egyptian view, despite the deadlock in the direct negotiations, there have been several favorable developments that strengthened Sadat's hand.

The invasion of Lebanon proved that the Arabs cannot or will not impose their will on Israel by force and therefore Sadat's chosen course, that of direct peace talks, is the right one.

It also showed, the Egyptians say, that the only way to get anything for the Palestinians is to persuade Israel that this is the only path toward peace - the Israelis learned they could not suppress the Palestinians by force and the Arabs hardliners showed te emptiness of their blustering about the Palestinian cause.

"There can't be any more talk of a separate peace between us and Israel," a senior official here said, "not just on moral grounds but because it won't work. Even if we had full peace with Israel and ambassadors in each other's capitals, things like the PLO bus raid will still happen unless there is peace on all of Israel's borders."

Egypt was gratified by the decision of Saudi Arabia to send its foreign minister, Prince Saud Faisal, to an Arab League Conference in Cairo that was boycotted by the hardline Arab rejectionists. The Egyptians feel that this shows they have at least the acquiescene of the Saudis in their peace policy, and that the rejectionists are as isolate politically as they are impotent militarily.

In addition, the Egyptians think the Israelis are losing the battle for American support. One reason for their effort to stay on good terms with Weizman is the belief that Prime Minister Menachem Begin, whom the Egyptians regard as a fanatic, may be ousted because he is jeopardizing Israel's traditional ties to the United States.

The cumulative effect of these assessments is to leave the Egyptians believing that the peace initiative can and should go on, if they will stay calm and keep to their course, which they say they are determined to do.

In Sadat's words, it is "the will of the people."