JERUSALEM, JUNE 3 -- Israel's most important and prestigious foreign assignment -- the job of ambassador to the United States -- has become a pawn in the battle over who controls the country's foreign policy and a symbol to critics of the paralysis gripping the coalition government here.

For the past eight months, Prime Minister Yitzhak Shamir, who heads the rightist Likud, and Foreign Minister Shimon Peres, leader of the left-leaning Labor Alignment, have been unable to agree upon a candidate. Meanwhile, the previous ambassador, Meir Rosenne, originally scheduled to leave in January, departed this week, leaving a glaring and embarrassing hole at the top of Israel's largest foreign embassy.

Although Shamir has dismissed the vacancy as "not a major tragedy," analysts here say that the pressure is on him to fill the post quickly to demonstrate that the "national unity" government he heads is still functioning and viable.

"Maybe it's not a tragedy, but it is an unpardonable sin," said Gideon Raphael, former director general of the Foreign Ministry. "They're not only slighting the United States but injuring Israel's vital interests. Mr. Shamir's tactic is to outwait and outwit Mr. Peres but in the process we are outwitting ourselves."

The ambassador's post for several months was held hostage to local politics. But in recent weeks the dispute has become a test of wills between the two leaders over whether Israel is prepared to participate in an international conference on Middle East peace. Peres supports the concept as a means of opening direct talks with Jordan, while Shamir is vehemently opposed and neither man appears ready to accept as ambassador a candidate wedded to the stance of his rival.

"The fact is that Israel has at the moment two competing foreign policies and a government in a crisis, and this appointment is a victim of all that," said political scientist Eytan Gilboa.

The dispute reached its nadir three weeks ago after Peres backed away from a showdown on the proposal because he lacked a majority in the policy-making inner cabinet. The Foreign Ministry then refused to convey a Shamir message to Israel's embassies saying the conference idea was dead, substituting instead its own telex insisting that the government still supported the proposal. Eventually a second, compromise cable was dispatched summing up both sides in the dispute.

Peres and Shamir have ruled jointly since the two major parties failed to achieve a functional majority in the Knesset in the 1984 elections. For the first 25 months Peres was prime minister and Shamir foreign minister. Last October they rotated offices under the 1984 agreement.

As part of the rotation, Shamir consented to choose a nominee from names submitted by Peres. Peres submitted a total of nine candidates, all of whom Shamir rejected -- an action Peres contends is a violation of their understanding.

Shamir's people say Peres' lists contained political figures, many of them more notable for their loyalty to the foreign minister than for their diplomatic experience or national stature. Among them were a Labor Party Cabinet minister, Gad Yaacobi, and two members of Peres' own staff, Yossi Beilin and Nimrod Novik. Shamir had in mind a senior Foreign Ministry official, Hanan Bar-On, rejected by Peres, who said he wanted "fresh ideas" in the post.

For months Shamir also insisted that he would not accede to one of Peres' candidates for ambassador until the foreign minister agreed to restore a Shamir political ally, Yitzhak Modai, to the Cabinet. Peres, while prime minister last year, had fired the flamboyant Modai, former finance and justice minister, after Modai had personally criticized him.

Shamir dropped that demand two weeks ago in an effort at reconciliation after he managed to muster the votes to deny Peres a majority in the inner cabinet or the Knesset to support the conference proposal or to call new elections. Shamir's aides now say he hopes to have the matter cleared up within the next few days and is willing to accept any "reasonable" candidate Peres might propose.

Others are not so certain the dispute is near resolution. As The Jerusalem Post noted in an editorial yesterday, the ambassadorship has become a "hardship" post, given the deep divisions within the government. Both Peres and Shamir have tended to circumvent Rosenne, dispatching members of their own entourage to Washington to explain their views -- and undercut each other. Peres had been especially blatant in insisting that Rosenne not attend private sessions between Peres and Secretary of State George P. Shultz.

"Systematically ignored by {Peres} and thus embarrassed vis-a-vis the U.S. government agencies with which he had to deal, Rosenne was forced to preside over the radical devaluation of the embassy," said the Post editorial. "As a professional diplomat he kept a stiff upper lip. But U.S. officials and American Jewish community leaders did not conceal their astonishment and dismay at the treatment he received."