The United States today gave Israel detailed, written proposals for security arrangements in southern Lebanon that would be part of an agreement for an Israeli troop withdrawal from its northern neighbor's territory.

U.S. Ambassador Samuel W. Lewis gave the proposals to Foreign Minister Yitzhak Shamir this morning. Shamir later briefed Prime Minister Menachem Begin on the ideas and on his round of talks in Washington with President Reagan, Secretary of State George P. Shultz and others that produced the latest U.S. initiative to break the negotiating deadlock.

The Israeli Cabinet may react to the American proposals at its next meeting on Sunday. Israeli officials were cautious in discussing the proposals, but there was no expectation that Israel would accept them without seeking additional concessions.

Asked on television last night whether Israel had given up its demand for the establishment of five Israeli-manned outposts in southern Lebanon after its other troops had withdrawn, Shamir said, "We have not given up anything. We presented our positions and American proposals were made to us in Washington , which are still unsatisfactory."

Apparently anticipating the written version of the proposals conveyed to him today by Lewis, Shamir added, "We are looking forward to additional proposals. We will discuss the entire complex of our demands in the issue of security arrangements and joint Israel-Lebanon relations, and decide accordingly."

The key issue in the deadlock over the security arrangements is whether Israeli combat forces will play any role in policing a 25- to 30-mile-deep "security zone" in southern Lebanon that Israel is demanding be established as part of a troop withdrawal agreement. Israel at first demanded a permanent presence in the security zone in the form of the five outposts, but more recently officials here have indicated their willingness to accept active joint Israeli-Lebanese Army patrols in the area instead.

But Lebanon, with the backing of the United States, argues that this would still amount to an unacceptable infringement on Lebanese sovereignty and has rejected the idea.

In their talks with Shamir in Washington, Reagan administration officials made a number of suggestions to try to get around this point in the negotiating deadlock. They include an expanded U.S. military role in Lebanon, accelerated U.S. training of antiterrorist units in the Lebanese Army, increased aid to Israel and Lebanon, an enhanced role for U.N. or multinational force units in southern Lebanon and the creation of an Israeli-Lebanese-U.S. commission to monitor the security zone.

The Cabinet's reaction to the U.S. ideas is expected to provide some of the first concrete clues to the attitudes and extent of influence in the government of Moshe Arens, Israel's new defense minister. Arens' predecessor, former defense minister Ariel Sharon, was a strong advocate of the outposts idea and will almost certainly oppose any proposals that do not give Israeli soldiers an active role in policing southern Lebanon.

It was not until Sharon was forced to leave the Defense Ministry because of the findings of the Israeli commission that investigated the massacre in Beirut of Palestinian refugees that Israel began to back off from the idea of outposts and suggest it would accept joint patrols. Arens has been described here as more eager than Sharon to achieve a troop withdrawal agreement, believing that Israel is paying too high a political price for its continued presence in Lebanon. But he has not made public or tested within the government his ideas on how Israel should go about this task.

Some of the obstacles to Israeli acceptance of the package delivered by Lewis were underscored by a senior official who briefed foreign correspondents today.

The official said Israel believes the Lebanese Army, on its own, is incapable of providing security in southern Lebanon and will remain so for two or three years at least. At the same time, the official said, Israel remains adamantly opposed to allowing U.N. or multinational forces to play a role in policing the security zone along with the Lebanese.

"This objection has not changed, and it was made clear to the Americans," he said.

The Israeli said U.S. officials accept the idea that there must be close Lebanese-Israeli cooperation in the security zone, but he suggested that there remain differences over what form this cooperation should take.

He also said the U.S. proposals do not deal directly with the future role of Saad Haddad, a former Lebanese Army major who is allied with Israel. Israel wants Haddad to remain in command of troops in southern Lebanon, but the Lebanese government objects to this.