After weeks of squabbling, the United States and Israel yesterday announced an agreement aimed at clearing the way for four European nations to participate in the peace-keeping force that will police the Sinai Peninsula after Israel returns that territory to Egypt next April.

The accord was approved by the Israeli cabinet yesterday and appeared to ward off Israel's threat to veto participation by Britain, France, Italy and the Netherlands because of their adherence to a European Economic Community initiative on the Middle East that the Jewish state finds unacceptable.

Israel's acceptance of the agreement followed daylong negotiations here last Friday between Secretary of State Alexander M. Haig Jr. and Israeli Foreign Minister Yitzhak Shamir.

It marked a big victory for the Reagan administration, which has been anxious that the proposed 2,400-man peace-keeping force have broad international representation rather than be an almost exclusively American operation. Even if several nations participate, the United States is expected to contribute approximately half of the troops in the force.

Until now, only three small countries--Uruguay, Colombia and Fiji--had agreed to contribute token units to the force. With the Europeans taking part, the force will have significantly greater status in the international community, and their participation is expected to lead to a further broadening of the force's multinational character by bringing in Australia, New Zealand and Canada. In essence, the agreement acknowledges that disagreements remain about the European approach to resolving the Palestinian issue and pursuing a comprehensive settlement of the Arab-Israeli conflict.

But it also says that, where the Sinai force is concerned, the European countries agree to participate on terms governed by the 1979 Egyptian-Israeli peace treaty and will attach "no political conditions" such as those in the EEC initiative.

In approving the joint announcement, Israeli Prime Minister Menachem Begin's cabinet specified that it expects the four European governments to state their acceptance of these principles. Whether the Europeans will be willing to do that publicly was not clear yesterday, but a senior U.S. official, who declined to be identified, implied strongly that European agreement has been arranged.

The official said the joint statement worked out by Haig and Shamir had been based on a message sent to Washington by the Europeans on Nov. 26. He added that it is "more than a reasonable expectation that in the near future we are going to have an agreed basis" for European participation in the force.

Underlying the dispute has been Israel's insistence that any moves toward Mideast peace be anchored in the 1978 Camp David accords, which produced the Egyptian-Israeli treaty and which currently are centered on negotiations between the countries over autonomy for the Palestinian inhabitants of Israeli-occupied territories.

Last year, the EEC, to which the four European nations belong, issued a declaration in Venice calling for a broadening of the peace process that would include "association" for the Palestine Liberation Organization. Israel vehemently opposes any role in the peace talks for the PLO.

When the European governments initially signified their willingness to join the Sinai force, they issued statements reaffirming their commitment to the EEC initiative. In response, Begin threatened to veto their participation on the grounds that it implied an attempt to change the Camp David process along the lines advocated by the EEC.

That led to a month-long flurry of negotiations involving Washington, Jerusalem and West European capitals that culminated in the talks last Friday between Haig and Shamir. They worked out the statement that, following some minor modification, was made public by the two governments yesterday.

It states that the clarifications provided by the four European governments show "that they recognize that the function of the Sinai force is as defined in the relevant Egyptian-Israeli agreements" and that the Europeans "have attached no political conditions, linked to Venice or otherwise, to their participation."

Then, in language that permits the Europeans to reserve their positions on Mideast policy moves beyond the scope of the Sinai force, the statement said the United States recognizes that some positions set forth by the Europeans in explaining their decisions to take part in the Sinai force "are at variance" with U.S. and Israeli views.

It added: "The United States and Israel recognize that the positions held on any other aspects of the problems in the area by any state which agrees to participate in the Sinai force do not affect the obligation of that state to comply fully with the terms" of the Egyptian-Israeli peace treaty.