Israeli Prime Minister Menahem Begin's surprise visit here was viewed by U.S. officials as an effort to hold on to the old dependent relationship with Washington that has been radically transformed - perhaps ended - by the dramatic Sadat-Begin diplomacy.

By rushing here to discuss his new peace plan for President Anwar Sadat, Begin was telling the Americans: Nothing has changed; we still rely on you. In word and nuance, the Americans here were replying: Everything has changed; you now stand on your own feet face-to-face with the Arabs; tell them your proposals for a settlement.

Two days before he arrived here, newspapers in Jerusalem hinted that Begin's visit was part of a broader Israeli-Egyptian scheme. When it became clear Sadat was as surprised as the United States, officials here were so annoyed that word was quietly passed: Begin is coming totally on his own initiative, with no Egyptian connivance.

That is just one clue to the new relationship between the United States and Israel. Although the United States naturally looks to Israel as its initmate friend, direct Israeli-Egyptian negotiations have suddenly ended a full decade during which Washington alone spoke for Israel in negotiations, a period during which the United States acted (in the phrase of former Defense Secretary Melvin Laird) as "Israel's attorney."

The sudden termination has led the Israeli government to seek new ways to keep the United States hitched to its side in negotiating with the Arabs. That is understandable, but it is something President Carter does not want.

At his press conference Carter carefully circumscribed any effort by Begin to pin down the United States as a negotiating partner at the Cairo conference. "I would not be the ultimate judge of whether or not it's [Begin's plan] acceptable or not to the Egyptians," the President said. "That would be up to President Sadat."

But conflicting with Carter's wise refusal to put the United States back in the umpire's seat is growing pressure from Israel's political allies in this country to resist any U.S. move to a truly neutral posture. That helps explain the President's quick assent to Begin's self-invitation, and Carter's request after their meeting Friday for Begin to stay an extra day. As one Mideast planner told us: "The last thing Carter wants is to give Begin, Israel or the American Jewish community the impression that Begin got the bum's rush here."

Begin holds high cards in his maneuvers to make it appear that the United States is still "Israel's attorney." During lunch at Blair House Friday, Begin confided details of his peace plan to four of Israel's staunchest friends in the U.S. Senate: Jacob Javits (R-N.Y.), Richard Stone (D-Fla.), Henry M. Jackson (D-Wash.) and Clifford Case (R-N.Y.). This preceded direct Israeli word to Sadat of Begin's plan. News was rushed to Cairo not by the Israelis, according to administration officials, but by telephone from the White House immediately following the first Carter-Begin talk.

The obvious explanation of Begin's decision to confide his plan to Carter and four U.S. senators before explaining it to President Sadat: maintain the pretense that the United States is still in its old role of attorney.

Carter's intent is different. He wants to maintain a certain distance from Israel (and, of course, the Arabs) while exploring several new ideas with his own advisers. One is a possible security pact not only with Israel, which has always been in prospect, but also with Israel's new talking partner to the West, Egypt.

With Israel facing Egypt directly across the bargaining table, Carter is comfortable with his new independent role. He seems to be distinctly enjoying the prospect that Israel will now carry the responsibility for hammering out peace on its own, a responsibility not affected by Begin's sudden visit.