When Robert S. Strauss was summoned to President Carter's White House office three weeks ago, he suspected he was going to be asked to run the president's 1980 re-election campaign.

But instead of asking Strauss to dust off his old Texas politician's Stetson, the president offered the Dallas lawyer a homburg to add to the many hats he has worn in the Democratic Party and the Carter administration.

That, Strauss recalled at lunch with reporters yesterday, was his first indication that Carter wanted him to take on the sensitive job of chief U.S. mediator in the next stage of Middle East peace talks between Israel and Egypt.

Strauss, who has been serving as Carter's trade negotiator, told the president that once the administration's foreign trade bill makes its expected way through Congress this summer, he wanted to return to Texas.

When Carter said he had something "far more important in mind," Strauss, who thought he was talking about managing the 1980 campaign, replied that the president needed a younger man.

Carter shot back: "I've got something far more important in mind than my or anyone else's political future. I have in mind peace in this world."

At that point, Strauss said, he blinked and told Carter, "I think I missed something here."

Then, Strauss added, Carter suddenly was urging him to accept the Middle East job. Although Strauss said he was reluctant at first, he finally agreed to make a quick trip to the Middle East to see how he worked "one on one" with Egyptian President Anwar Sadat and Israeli Prime Minister Menachem Begin.

In the end, everyone involved agreed that the chemistry generated on that trip two weeks ago was promising and Strauss's appointment as ambassador-at-large was announced Tuesday night.

Strauss said that winding up the trade bill won't permit him to get into the peace talks full time until after Labor Day. He left no doubt, though that one he does get going he plans to hit the Middle East running flat-out in the highly visible, free-wheeling style that characterized his performances as Carter's trade negotiator, as inflation czar and as chairman of the Democratic National Committee.

"As you know, I'm a meddler and a self-admitted expert in a number of fields that there's some question about," he said. And, while admitting that he's got to do a lot of boning up on the intricacies of the Middle East situation, Strauss noted pointedly: "I'm a very fast learner."

He also hinted strongly that his approach to the mediator's job is likely to be very different from that of his predecessor, Alfred L. Atherton Jr., a relatively anonymous career diplomat whose role was delineated clearly as that of a lieutenant to Secretary of State Cyrus R. Vance.

By contrast, Strauss made clear that he doesn't see himself as a State Department underling. Referring to his present location in a suite next door to the White House, he said. "I'm comfortable where I am."

Elaborating on that point, he went out of his way to stress his respect for Vance's authority in foreign relations matters and said he viewed his relationship with the secretary of state as a "partnership" where he would always seek Vance's "advice and consent." He added:

"As Cy knows, I'm not a fellow who works very well for another fellow."

The question of how much autonomy Strauss will have in the negotiating process has already raised some eyebrows at the State Department. Although Strauss said Carter had told him that all the key administration officials involved were enthusiastic about his appointment, Vance is known to have recommended that the job go to former United Nations ambassador William Scranton or former national security affairs adviser McGeorge Bundy.

But, while conceding that some "awkward" lines of authority need to be worked out, Strauss insisted that he doesn't see any potential for conflict with Vance. Responding to questions about whether he would work from the State Department or the White House, he said: "It doesn't make much difference where you are. It's what you do when you get there."

In fact, he added, the principal reason for his assuming the mediator's job was to free Carter and Vance from the heavy demands made on their time and attention by the many crises encountered in the first phase of Egyptian-Israeli negotiations.

"I wasn't picked for this job because of any background or expertise. It was because of my relationship with the president-my ability to communicate with him quickly and easily in shorthand and to understand what he wants done," Strauss said.

Pointing to his recent visit to the region, he said his efforts already have set in motion the possibility of increased private U.S. investment in Egypt and said:

"That was done by Bob Strauss who didn't want to go in the first place but who's now an expert after spending two days in Israel and Egypt and reading a book."

On a more serious note, Strauss said he was fully appreciative of the complexity of negotiations "where frustration is going to come in large bites and progress in inches."

And he also said: "Who knows? They may fire my a -- out of there in 30 days." CAPTION: Picture, ROBERT S. STRAUSS . . . "I'm a very fast learner"