The Israeli Cabinet's decision last week to begin a staged withdrawal from Lebanon marked an important milestone in the brief history of the national unity government here, solidifying Prime Minister Shimon Peres' leadership of the divided coalition government.

The ambivalence of the Israeli public toward the controversial war in Lebanon was reflected in last July's parliamentary election that produced a government split evenly between the Likud bloc and the rival Labor Party.

But now, just four months after assuming power as prime minister, Peres has put the stamp of the Labor Party on Israeli policy in Lebanon. When forced to vote, the Cabinet decisively chose the phased but total withdrawal policy of Labor against the Likud's insistence that Israel stand firm in Lebanon until it achieved what it considered adequate security guarantees.

While the partnership is uneasy, the Cabinet's 16-to-6 decision certified that Peres' Labor Party is dominant. The decision made Peres the clear winner on a key issue against the Likud leader, Foreign Minister Yitzhak Shamir.

Within the Labor Party, despite their long history of personal animosity, Peres and his party rival, Defense Minister Yitzhak Rabin, worked closely together to engineer the withdrawal decision. The strong support for the staged withdrawal plan by Rabin and the military was a decisive factor in gaining Cabinet approval. Moreover, Peres was able to give the decision a bipartisan cast by winning the support of two ministers from Likud and three from religious parties normally aligned with Likud.

The most important of these votes came from Deputy Prime Minister David Levy, a young, rising star in the Likud who has challenged Shamir's party leadership once and has indicated that he intends to do so again at the next opportunity.

The support by Levy and by Science Minister Gideon Patt of the Liberal Party wing of the Likud bloc gives Peres and the Labor Party some protective political covering should the withdrawal go badly and there be a renewal of terrorism along Israel's northern border.

In contrast, Shamir, who was Israel's prime minister going into the last election, has never looked weaker. Besides failing to hold all the Likud ministers behind him in defense of Likud policy in Lebanon, he suffered two other setbacks last week that may have longer term consequences for his political future.

One of these occurred in New York, where Shamir's party rival, former defense minister Ariel Sharon, won on the first two of the four issues put to the jury in his libel suit against Time magazine. Regardless of the jury's verdict on the other two issues, the first two decisions almost certainly will strengthen Sharon's hand as he, like Levy, plots to overthrow Shamir as the Likud leader.

The second setback came in Israel's parliament, which by a 62-to-51 vote defeated an attempt by religious parties to amend Israeli law to recognize only Orthodox conversions to Judaism. The Labor Party opposed the measure, while a solid majority of Likud, seeking to maintain its alliance with the religious parties, voted for it.

But after the vote, the wrath of religious party leaders was directed not at the Labor Party -- from which they had not expected support -- but at the Likud for not providing as much support as promised. Again, Shamir was seen as having failed to deliver.

The personal political fortunes of Peres and Shamir are closely intertwined because of the unique agreement between them that led to formation of the national unity government. Under that accord, midway in the government's normal four-year term, in September 1986, the two men are to switch jobs, with Shamir becoming prime minister and Peres taking over as foreign minister and vice prime minister.

Virtually no one in Israel believes that Peres has any intention of going through with the deal. Sometime in the next 12 to 16 months, it is widely expected, he will attempt to bring about an open rupture in the national unity government. A walkout from the government by the Likud would nullify the power-sharing agreement with Shamir and give Peres a chance to form a new, narrowly based coalition under Labor. Failing that, it would force elections, in which Peres would have the great advantage of being the incumbent prime minister.

In bringing about a Lebanon withdrawal decision in keeping with the Labor Party's election promises, Peres appears to have strengthened his position in the coming political maneuvering. Left-wing critics of Labor's decision to join in a government with the Likud have largely been silenced. For the moment, Peres, despite his lackluster record when he was opposition leader, appears safe from serious internal challenge as Labor Party leader.

Shamir, in contrast, must more than ever keep looking over his shoulder at politically strengthened Sharon and Levy as he attempts to hang on long enough to regain the post of prime minister.