It was time to break the ice with the prime minister of Israel and Robert S. Strauss was launching into the kind of bright personal anecdote that has helped him build a highly successful career in Washington as raconteur, politician and negotiator.

Sitting down for his first business meeting with Menachem Begin and about to hand a personal message from President Carter to the Israeli leader, Strauss was telling Begin about his grandmother's habit of continuing to read letters "even when we would come into the room."

"What about the letter I sent you?" Begin shot at Strauss. "Did you get it?"

Taken aback for one quick beat, Strauss suddenly remembered the letter and switched to talking about it. As reporters were shooed from the meeting room, the grandmother had disappeared from the conversation and Strauss, President Carter's new Middle East peace negotiator formally began his first day on the job

Throughout a day of meetings, Israeli officials appeared to welcome Strauss with a brisk, businesslike approach and standard reiterations of their negotiating positions rather than trying to break new ground.

Shortly after sunset, Strauss met briefly with reporters and said he had been impressed during "a reasonably good day" with Israel's readiness to start working on "the practical, hardnut problems" in the Egyptian-U.S.-Israeli negotiations on Palestinian autonomy on the occupied West Bank.

As described by Strauss, the Carter letter to Begin contains a generalized expression of confidence "that we can make progress" and a strong statement of support from Carter for Strauss. "I guess he figured I needed all the help I can get,''' Strauss said.

Strauss flies to Alexandria Tuesday to meet Egyptian President Anwar Sadat and take part in the three-nation negotiating session that has been unable thus far to come up with an agenda of the topics for Egypt and Israel to discuss. He said the day's meetings reinforced his view that the autonomy talks would be "a slow step-by-step thing" and "a long hard pull."

The impression of calculated Israeli restraint in welcoming Strauss as Carter's special representative was underlined in Israeli newspapers and radio broadcasts that gave more prominence today to the nearly simultaneous arrival here last night of Henry Kissinger, the man who first ran the step-by-step Middle East approach Strauss referred to and may now seek to copy.

A photograph of Kissinger and Sen. Henry Jackson (D-Wash), both here to receive honorary degrees from the Hebrew University, dominated the front page of Monday's edition of the Jerusalem Post.

Kissinger, who has emphasized the private nature of his trip, flew into Israel on an Egyptian presidential jet provided by Sadat, who hosted Kissinger and his wife Nancy at a lawn dinner in Alexandria Saturday night. The paths of the former secretary of state and the new American mediator almost crossed several times today as Kissinger called on many of the same people Strauss saw, including Begin.

Strauss did not see Foreign Minister Moshe Dayan, who was released from a hospital today following the removal of a maliganant tumor. Accompanied by his State Department aides, Strauss attended a late afternoon meeting with the Israeli negotiating committee chaired by Interior Minister Josef Burg.

Speaking informally to reporters later, Strauss three times praised the work being done for him by State Department specialists, "to dispel the notions" mentioned in Israeli and U.S. newspapers "that Bob Strauss and the State Department can't get along."

Strauss, who carries the rank of ambassador-at-large for this Middle East assignment, said that he had restated the administration's strong opposition to Israeli settlements on the West Bank - "That is my position also" - and had been told in return of Israel's long-standing rejection of that position. "It was the nearest thing to a draw you've ever seen," he said.

Asked if the United States had developed its own definition of Palestinian autonomy to present at the talks, Strauss said, "I would hope never have to have one. I would hope the parties will work one out on their own." CAPTION: Picture, Israeli Prime Minister Menachem Begin greets U.S. Sen. Henry Jackson with a hug. AP