JERUSALEM, JUNE 7 -- The Cabinet today approved the nomination of career diplomat Moshe Arad as Israel's ambassador to the United States, ending a six-month deadlock over the country's most important foreign posting that had become an embarrassing symbol of this government's deep political divisions.

Arad, now ambassador to Mexico, was nominated last week by Foreign Minister Shimon Peres and endorsed over the weekend by Prime Minister Yitzhak Shamir, according to the prime minister's office.

A formal announcement of the appointment will follow State Department approval, which is expected.

The Cabinet decision follows the departure a week ago of ambassador Meir Rosenne, whose term in Washington was supposed to end last January but was extended because Shamir repeatedly rejected candidates put forward by Peres, his main governing partner.

Shamir leads the Likud coalition and Peres the Labor Alignment, the two major political blocs in the 33-month-old coalition government.

The two men are locked in a sharp dispute over Peres' advocacy of an international Middle East peace conference as a forum for convening direct talks between Israel and Jordan. Peres argues that the conference is necessary to provide a cover that will allow Jordan's King Hussein to hold bilateral talks with the Israelis without being branded a traitor to the Arab cause, while Shamir contends Israel will be pressed to abandon all of the territories it has occupied since 1967 and its security will be threatened.

The dispute has paralyzed the country's major embassies abroad on the issue, left Israel with two irreconcilable foreign policies and further divided the governing coalition. Both leaders have bypassed Rosenne and the Washington embassy in recent months, sending personal envoys to meet with State Department officials or conveying conflicting messages through U.S. Ambassador to Israel Thomas Pickering.

The Israeli Embassy in Washington is involved in a legal battle between Israel and Special Prosecutor Lawrence Walsh over his efforts to obtain direct testimony from four Israelis involved in the Iran arms affair. Walsh has subpoenaed the four following Israel's insistence that all information be supplied on a "government-to-government basis" and not by the individuals involved.

Peres and Shamir have ruled jointly since inconclusive national elections in 1984. Under their coalition agreement, Peres as foreign minister was to propose names for the ambassadorial post subject to Shamir's veto.

Shamir rejected nine names put forth by Peres, all of whom had close ties to Peres or his party. Shamir demanded a professional diplomat and for a time also insisted on the return of a political ally to the Cabinet.

Several prospective nominees turned down consideration for the post because they felt they could not function effectively on behalf of a government so divided.

Arad, who has spent 25 years in the Foreign Ministry, has less public stature than many of those mentioned in the past for the post, some officials here say. But he was considered a workable compromise because he is known to be a Labor supporter but also has a reputation as a highly competent professional diplomat.

"His major qualification is the fact that he got those two people {Peres and Shamir} to agree," said Abba Eban, who has been both foreign minister and ambassador to the United States.

"He'll take a professional view," said Eban, "but it's a pretty impossible job when his prime minister is saying that no one should take any notice of what the foreign minister is doing when the ambassador works for the foreign minister."

Peres raised pressure on Shamir to accept a suitable candidate last week by refusing to reextend Rosenne's term.

The prime minister, who wants to keep his office until the next regularly scheduled election in October 1988, has argued that the coalition government is still functional and worth preserving despite the dispute over the peace conference. Peres, on the other hand, is seeking early elections, and his supporters used the Washington vacancy as an example of the coalition's paralysis.

Shamir approved Arad after a meeting last night between the two men, according to the prime minister's spokesman, Yossi Achimeir.

"He {Shamir} knows Arad very well from the time when he was foreign minister," said Achimeir.

Playing down claims that Arad is a Labor supporter, Achimeir added, "We hope that he will be neutral and represent all of the government and not part of it."

Arad was born in 1934 in Romania and emigrated to Israel in 1950. Before becoming ambassador to Mexico in 1983, he served in Israeli embassies in Washington and London and in the consul general's office in New York. He has also held several senior posts at the Foreign Ministry here.