VICE PRESIDENT MONDALE'S mission to the Middle East has not entirely revived the Mideast peace movement. But it has supplied some badly needed artificial respiration - against very difficult odds. By the time the Mondale party set forth, the vital signs of promising movement toward Mideast peace were, in a word, weak. U.S.-Israeli relations were uncommonly strained. The fears of many Israelis of American abandonment, tracing back to the joint Soviet-American call last fall for a renewed Geneva conference, had been more recently reinforced by the sale of U.S. warplanes to Saudi Arabia. Many leading Israelis sensed a thinly disguised conviction on the part of the Carter administration that the peace movement could never really progress while Mr. Begin remained in power.

And the mission was made no less difficult by the fact that what had originally been planned as largely a ceremonial participation in Israel's continuing celebration of its 30th anniversary had become inevitably caught up in efforts already under way, on separate diplomatic tracks, to promote a resumption of direct negotiations between Israel and Egypt.

It thus became necessary for the vice president not only to discharge the ceremonial functions, to attempt to reaffirm in convincing fashion the depth and durability of the American commitment, but also to seek to put to rest as convincingly as possible the suspicions of a good number of Israelis of an American inclination to interfere in internal Israeli politics by trying to undermine the authority and even the power of Mr. Begin. And he had to do the latter while at the same time trying to prod the Begin government as firmly and forcefully as possible into a positive and constructive approach to the resumption of negotiations with Egypt.

Mr. Mondale's multiple purposes were painfully complicated by an unexpected - and, one would like to believe, inadvertent - contribution by President Carter himself. In the course of a question-and-answer session with out-of-town editors last week, Mr. Carter delivered himself of some observations about the state of affairs in the Middle East that, when publicly released over the weekend, could hardly have been less helpful to the delicate work in which Mr. Mondale was engaged.

The Vice President, Mr. Carter was quoted as telling the editors, was "doing some symbolic things to show the Israeli people we genuinely do care about them" - a characterization of the vice president's undertakings that would have been a little cynical even for an internal planning memo between bureaucrats. Gratuitously, he restated his "disappointment" with Israeli's recent bargaining position. Casually, he offered his "guess" that an Egyptian proposal, which actually was handed to Mr. Mondale by Mr. Sadat in Alexandria on Monday, for transmission to the Israelis, and which the president obviously had yet to examine, would be a "step in the right direction, but inadequate" - a remark that, even with the benefit of later clarification, was taken by many Israelis in their present injured, sensitive state of mind as a reflection on their intransigence.

And, finally, before the hoped-for resumption this month of direct negotiations between Israeli and Egypt had even been ensured, he held out the prospect of a renewed Geneva conference, an idea that almost nobody except the Soviet Union and the more extreme Arab states is in favor of, as a "fallback position."

We recite all this background merely by way of explaining why we think that under all the circumstances the vice president's Mideast mission was a success. He persuasively reaffirmed America's unshakable commitment to Israeli security. He used the occasion to state in plain and forthright terms the principles that the United States think should be applied to any ultimate Mideast settlement. He helped prepare the ground, insofar as it was possible, for a resumption of negotiations sometime this month in London between Egypt and Israel at the foreign-minister level, with the United States on hand. He made no bones about the difficulties ahead and the large differences that will have to be bridged.

Perhaps most important, he apparently took more than one opportunity to stress the importance of a return to quiet, private, face-to-face diplomacy, as distinct from diplomacy "in the context of public declarations" - a prescription that we think is as appropriate to Mr. Carter as it is to Mr. Begin and Mr. Sadat.