Amid deepening political trouble for his defense minister, Ariel Sharon, Prime Minister Menachem Begin was reported today to be ready to give in to demands that a State Judicial Board of Inquiry be established to investigate the massacre of Palestinian refugees in Israeli-occupied West Beirut.

A number of Begin's political associates, including the leaders of three parties in his government coalition, are demanding such an investigation, and Justice Minister Moshe Nissim said today it appears the Cabinet will have no choice but to agree to the high-level inquiry when it meets Tuesday.

Begin was quoted today as saying he had opposed the convening of a State Judicial Board of Inquiry, the most powerful investigative panel allowed under Israeli law, because such a panel should be reserved for "only the most serious wrongdoing." He denies Israel bears any responsibility for the massacre, but he was said today by Israeli radio to be on the verge of proposing a judicial board of inquiry himself because of the dissension within the Cabinet and the public pressure.

Meanwhile, speculation increased that a judicial board of inquiry could spell the beginning of the end for Sharon, who is under renewed attack for recent comments that offended his subordinates in the military, the political opposition and colleagues in the Begin Cabinet.

Sharon set off the uproar during a parliamentary debate last week when he asserted that when the opposition Labor Party was in power in 1976 the Israeli Army played some unspecified role in a massacre of Palestinian refugees by Lebanese Christian militia units at the Tal Zaatar refugee camp in Beirut.

The accusation was vehemently denied by Labor Party leaders who headed the government at the time and prompted a retired Army general who was responsible for contacts with the Christian militias also to deny it.

"Whether we like it or not, an accusing finger is being pointed at the Army, and we're being accused of things of which the Army is completely innocent," said Gen. Ginamin ben-Eliezer, secretary general of a small political party that is part of Begin's government coalition.

Sharon's statement was aimed at his bitter enemies in the Labor Party, but it has been widely interpreted here as a smear on the Army, which is already reeling from charges of complicity in the massacre of Palestinian refugees last week in the Shatila and Sabra neighborhoods of West Beirut.

"Many people around Begin realize that what Sharon said about Tal Zaatar is simply unacceptable in terms of Israeli public life," said one senior official.

The defense minister then appeared to compound his own problems by two comments during a television interview Friday night.

Sharon acknowledged during the interview that Israel's announced intention in sending its troops into West Beirut earlier this month -- to prevent anarchy in the wake of the assassination of Lebanese president-elect Bashir Gemayel -- was merely a "smoke screen" to hide its real purpose of rooting out the remaining Palestinian guerrillas in the city.

This comment, according to reports in the Israeli press, has greatly weakened Sharon's standing among other Cabinet ministers who see it as implicating them in a deliberate attempt to deceive the public.

During the same interview, Sharon said that earlier in the war in Lebanon an elite paratroop unit that was about to be mobilized was not called up after senior military officials concluded that dissension within its ranks over the war would have made it ineffective.

In the context of Israeli reverence for the military and the tradition of military service in the country, this was an extraordinary admission by a defense minister and appeared to many to be another sign of deteriorating morale in the Army under Sharon's leadership.

As a result of these comments, the Israeli parliament is being called into another special session Thursday by the Labor Party to debate the Tal Zaatar accusation and the case of the reluctant paratrooper unit. The Labor Party was turned down on a demand that the parliament also debate whether the Begin government should resign on the grounds that a confidence vote in the government can only be raised during the regular session, which begins in mid-October.

Begin is still thought unlikely to oust Sharon, although he has the power to do so under a law enacted last year. Those who believe that Sharon will survive, at least for a while, point to Begin's strong sense of loyalty to political associates and the fact that the dismissal of the defense minister now would be interpreted as an admission of guilt by the Israeli government in the refugee massacre.

But whether Sharon could survive the scrutiny of a judicial board of inquiry armed with subpoena power is another matter, particularly in light of his weakened political standing.

"I think there are many ministers and other members of the Likud Begin's coalition who now see Sharon as a definite liability," one official said.

The turmoil in the Army continued following the acknowledgements last week that it coordinated and assisted the entry of Christian Phalangist units into the Beirut refugee areas where the massacre occurred.

The military command announced that Chief of Staff Rafael Eitan had rejected a request from the commander of the Army's command and staff college to be relieved of his duties because of the massacre. According to the announcement, Eitan told the commander, Gen. Amram Mitzna, to return to his post or leave the Army, adding that it was "inconceivable that an officer serving in the Army of a democratic country should concern himself with the appointment of government ministers."

Mitzna and an unnamed general who commands a combat division in the Beirut area met with Sharon Friday, reportedly telling him he should take responsibility for the events in the Lebanese capital and resign.

Eli Geva, the tank commander who was discharged from the Army earlier after resigning his command, saying he did not want to lead his unit into West Beirut because of the likelihood of high casualties, also continued to speak out. Geva was quoted as saying that he had warned Sharon and Eitan around the time of his dismissal that "they will cause a split in the Army."

Last week the Begin government sought a way out of the mounting domestic criticism that has been directed at it without resorting to a state judicial board of inquiry. It asked the president of the Israeli Supreme Court to conduct his own investigation, but the judge turned down the request because the court is considering two cases demanding the higher level inquiry.

The afternoon newspaper Yediot Aharonoth today published the results of a public opinion poll showing support for an internal investigation. The poll said 51 percent of the Israeli public favors a judicial board of inquiry and 23 percent a lower level examination, while 25 percent oppose any kind of inquiry into the incident.