The Israeli Cabinet began its often postponed debate on the future of the occupied West Bank yesterday, and said it will reach conclusions next week on key questions posed by the United States about the future of the territory under Prime Minister Menachem Begin's proposed five-year plan for self-rule.

While no decision was reached, the debate produced the government's first committment to providing the answers on a specific date, June 12.

The closed Cabinet meeting was held in response to questions posed by the State Department in April. It had been put off repeatedly, first because Israel sought to reassess its position following U.S. Senate approval of the sale of warplanes to Egypt and Saudi Arabia, and later because Begin was ill.

The Cabinet, according to Cabinet Secretary Aryeh Naor, spent some time establishing "procedural" rules for the debate, and although Begin and Foreign Minister Moshe Dayan participated, neither addressed the substantive issues directly.

The "procedural" issue, it later was learned, was an attempt by hardline supporters of Begin's policies to shut off the debate on the basis that Washigton's questions do not require soul-searching on the part of Israel and could be answered without extended discussion.

The United States had told Israel there would be little chance of reviving bilateral Egyptian-Israeli peace talks unless Israel is forthcoming with responses to two questions: whether a final settlement on West Bank sovereignty will be possible after five years of limited Arab self-rule, and how West Bank Palestinians will achieve a measure of political self-expression at the end of the five-year period.

Dayan's role in yesterday's meeting was of special interest because he and Begin reportedly have been at odds over broadening Begin's autonomy proposal for the West Bank in order to assign Jordan a more prominent role in governing the territory.

Dayan was said to have told Begin in private meetings that by providing an active role for Jordan in the self-rule plan, Israel could regain a measure of backing in Washington for its negotiating posture and put new pressure on Egyptian President Anwar Sadat, who has become increasingly aloof on the question of reopening the peace talks that ended abruptly in January.

Dayan reportedly made no attempt to present his proposal in the first debate but an informed source said before the session that the foreign minister would argue that Israel should provide the United States with more detail of what it ultimately has in mind for the West Bank.

Nothing has been officially disclosed about Dayan's ideas on a Jordanian presence in administering West Bank self-rule for the Palestinians. He is said to believe that by giving Jordan a role there will be less likelihood that at the end of five years the occupants would insist on the Palestinian Liberation Organization as their sole representative.

It remains unclear how Begin responded to the proposal in the private meetings, although according to the afternoon daily, Maariv, the prime minister rejected the idea in the belief that Israel should provide broad answers, only at the end of five years thereby avoiding the possibility of restricting its negotiating latitude now.

While refusing to characterize the debates of any of the ministers who spoke, Naor said, "It would be exaggerated to say that there were schools of thought. Nuances would be the right word."