Israeli political leaders today began feverishly counting heads in the fragile Likud coalition that controls parliament in an effort to determine whether Defense Minister Ezer Weizman's call for early elections has tipped the balance against Prime Minister Menachem Begin's beleaguered government.

Begin's Herut Party, the nucleus of the Likud, stiffly reprimanded Weizman for his statement on Israeli television last night that he supports elections before Begin's term ends in May 1981 and that he may serve as a defense minister in a Labor Party government.

Astonished leaders of the Herut, of which Weizman is a member, criticized the defense minister's prediction that Begin cannot last in power another year, and called it a clumsy attempt to thrust himself into the forefront of the race for the premiership. They were particularly critical that Weizman made the remarks while Begin was in Washington finishing up a round of Middle East peace talks with President Carter.

"There's a reason why rats always leave a sinking ship -- they bore the holes," one Begin supporter said bitterly.

Whether Begin's ship is actually sinking is by no means clear, and the prime minister has shown suprising buoyancy in the face of other political crises. But coupled with rampant inflation and a widely held public perception of a government aimlessly adrift in a sea of international and domestic problems, the latest challenge appeared to make the prime minister more vulnerable than ever.

Weizman, the popular former fighter pilot who managed Begin's campaign to an upset victory four years ago, stands far ahead of the premier in popularity polls, and his television remarks were widely interpreted as an attempt to bring down the government while he still enjoys that lead.

Begin so far has refused to comment on his defense minister's latest remarks, and some party strategists said the prime minister may decide to ignore the issue when he returns Friday from his U.S. trip.

Sunday and Monday are holidays, connected with Israel's independence, and Begin could decide to let the furor die down without risking a confrontation with Weizman.

Weizman, whose explosive personality is well known in Israel, has frequently predicted the collapse of the Begin government in not-so-private remarks in the corridors of the Knesset (parliament). Last night, however, was the first time he has called publicly for early elections.

Begin, apparently mindful of the thinness of his own support in the 120-member Knesset, previously chose to ignore Weizman's criticisms. The coalition has only a five-seat edge in the Knesset and it faces threatened defections from the 12-member National Religious Party and the six-member Democratic Movement Party.

Some of the more cautious members of the administration, including Deputy Prime Minister Simcha Ehrlich, warned against overreacting to Weizman's statements. One of the main unanswered questions today was whether cautious leaders of Herut and of the Liberal Party, which is also the Likud, could gain control and smooth over the controversy.

Yet the chairman of the Herut faction in the Knesset, Haim Kaufman, said he was "shocked" by Weizman's remarks, adding, "If Weizman is ready to serve under [a Labor Party government], he is no longer a political leader but a professional defense minister. That won't get him the premiership."

It is not unusual in Israel for major political figures to bolt to ideologically opposite governments, as former foreign minister Moshe Dayan did when he left the Labor Party for Begin's Cabinet.

A key factor in whether Begin's government can continue staggering from one bad week to the next is how the Religious Party and the Democratic Movement ministers react when the prime minister brings before the Cabinet a proposed law to enhance the legal status of Jewish settlements in the occupied West Bank and Gaza Strip and make them virtually immune to court challenges.

The controversial measure has already divided the Religious Party, with Interior Minister Yosef Burg and Religious Affairs Minister Aharon Abu-Hatzeira both opposed to it. The two men have also publicly backed early elections.

If the settlements protection bill becomes a catalyst issue for Begin's opponents, political observers say, it could cause enough defections to topple Begin's government even without Weizman's prodding.