Two weeks of constant and acerbic wrangling with Israel have revived a painful foreign policy dilemma for the Carter administration, which may finally have to decide if it sees Israel as the problem or the solution in the Middle East.

Irritated exchanges since mid-July about Israeli raids into Lebanon, U.N. peacekeeping forces and U.S. attitudes toward the Palestine Leberation Organization seem to have convinced the Israelis that the administration is reverting to treatment of Prime Minister Menachem Begin's government as a problem case after a period of relative calm.

The Israelis have responded sharply and have given signals that they are battering down for a full confrontation if necessary.

Underscoring its scorn both for Washington's denunciations and U.N. peacekeepers, Israel; announced yesterday that its troops sweep into U.N. policed areas of southern Lebanon overnight and kiled at least seven Palestinian guerrillas.

The atmosphere could worsen again on Sunday, when a decidedly pugnacious Israeli cabinet is due to take up Jerusalem's multiple disputes with Washington. Former prime mininter Yitzak Rabin said yesterday that it is TIME FOR Israel to "get tough" with President Carter.

Israeli irritation and concern and a fine appreciation of tactical positioning appear to lie behind these moves ad an accompanying increase in criticism of Carter by U.S. Jewish groups.

One effect of the repeated raids into Lebanon is to make it more difficult fr Yasser Arafat's branch of the Palestinian Liberation Organization to accept the conditions laid down by the United States for the opening of contacts, which key U.S. Arab allies, including Saudi Arabia, feel essential for j true Middle East peace.

The increase in domestic criticism also puts the administration on notice that it faces a major political upheaval on any opening it makes toward the Palestinians.

The informal policy discussions within the administration about how to respond to these pressures still are too diffuse to be called a major policy debate. But they are heading that way.

Put in simple terms, the State Department appears to believe that working around Begin's objections and getting Palestinians of all political stripes, including the PLO, involved in peace negotiations is the administration's most urgent task, which must be pressed now even at the risk of violent Israeli reaction.

Other officials emphasize avoiding a confrontation with Israel on the PLO issue now. They say they hope to persuade Begin to make some gestures on other issues that would improve the atmosphere both with the United States and Egypt, and convince the Palestinians, Jordon's King Hussein and the Saudis that it is up to them to catch up with a moving peace train.

This argument presents Israeli action as the solution to be sought through persuasion. It has the added advantage of appearing to reduce Carter's already substantial political problems between now and November 1980.

Not surprisingly, Carter's most experienced political aides, Vice President Mondale and special Middle East negotiator

Robert S. Strauss, are said by other officials to be partial to this approach.

Mondale yesterday sought to dampen Jewish criticism of reported remarks by Carter at a White House dinner Monday comparing the Palestinian movement with the U.S. civil rights movement. In at last eight telephone calls to America Jewish leaders and in an interview with Israeli television, Mondale retiterated that Carter's remarks did not indicate any change in U.S. policy toward the PLO.

Strauss is on vacation, and has stayed away from the dispures with Israel over the PLO and the U.N. peacekeeping force. In public statements during his trip to the Middle East last month and in published INTERVIEWS SINCE, Strauss has placed heavy stress on getting Palestinians involved in the autonomy talks, but he has carefully spelling out who or what he has in mind.

Diplomatic sources report that Strauss agrees with the State Department's view that some highly visible action is needed by the end of the year to give the talks it has to be the playing of the Palestinian card.

These sources report that Strauss proposed to Begin during their meeting in Jerusalem last month a unilateral Israeli gesture of good wil, such as declaring a halt to the attacks on Palestinian camps in Lebanon. This could cut Palestinian terrorism against Israelis and win Begin wider approval abroad, Straiss reportedly argued.

But Strauss' appeal to enlightened selfinterest appears to have the State Department's increasingly strident condemnations of the Israeli strikes.

"We will never get begin to buy the idea of a unilateral gesture," predicts an American who has, dealt extensively with the Israelis. "That is not how they operate."

The position of national security adviser Zbigniew Brzezinski in the American discussions is much more blurred today than it was before the Camp David summit, when the Israelis were accusing him of masterminding the confrontational approach.

Much of that suspicion seems to have evaporated, and Brzezinki met with Israeli Ambassador Ephraim Evron Thursday for 45 minutes, apparently in an effort to reassure the Israelis once again about U.S. intentions.

Discussions with U.S. and Israeli officials suggist that the most important single irritant of the past two weeks was the U.S. decision to patch together an agreement with the Soviet Union to use U.N. obsevers to police the Sinai withdrawal.

The agreement was described to Israel only after it was reached in Moscos July 13,. The Israelis, who have never been enthusiastic supporters of detente or the strategic arms limitation treaty (SALT) apparently felt their interests had been sacrificed for the purp0oses of detente, and they set out to strike back at Carter on a broam front.

The conflict was a mini-version of the uproar created by the October 1, 1977, U.S. Soviet communique on the Middle East. Israel saw the joint communique as bringing the Soviet back into the region gratuitously and increasing the likelihood of U.S. contacts with the PLO. The violent reaction caused Carter to back away from the communique and freeze any thought of cooperation in the Middle East with the Soviet until the U.N. peacekeeping arrangement was put together.

Rabin's call for a tough approach to the United States was contained in an article he wrote for an Israeli newspaper. The article noted that "President Carter's currently shaky status enables Israel to wage an effective fight for the favor of the U.S. public. . . ."

At the same time, Deputy prime Minister Yigal Yadin was quoted elsewhere as saying that the negotiations between Egypt, the United States and Israel over autonomy for the West Bank and the Gaza Strip would break down if the United States pushed for a broader definition of autonomy than Israel feels it agreed to at Camp David.

News agencies quoted Israeli officials as attacking proposals put forward this week by Strauss' State Department deputy James Leonard, who reportedly suggested that Palestinian legislative and judicial authorities should be created in the two territories after elections.