Few details of the massacre in Lebanon reported in the Israeli press, combined with Defense Minister Ariel Sharon's admissions of coordinating the Christian militia's entry into the refugee camps where the slaughter took place, produced mounting criticism today of Sharon and Prime Minister Menachem Begin.

The respected English-language Jerusalem Post in an editorial compared Begin's efforts to prevent a formal investigation of the massacre to Richard Nixon's stonewalling during the Watergate scandal. It again called for his resignation.

Sharon was greeted by several shouts of "murderer" and "monster" during the day when he spoke at an Army camp south of Tel Aviv at a memorial ceremony for paratroopers killed in Israel's wars, though many others at the ceremony voiced strong support for him.

About 3,000 people marched on Begin's home, chanting "Begin resign," The Associated Press reported. One of the marchers carried a placard depicting a snarling Sharon and reading, "Stop that monster."

The Israeli military command announced that a senior officer, Brig. Gen. Amram Mitzna, head of the Israeli Defense Forces staff college, asked today to be relieved of his duties "in consequence of the events of recent days in Beirut," AP said. Mitzna was the first officer to ask for indefinite leave as a result of the massacre; a colonel had resigned earlier in protest of the invasion of Lebanon.

Israeli radio said that 200 scientists from the Weizmann Institute, Israel's leading scientific research center, had sent a petition to Begin calling for an official investigation of the massacre.

While Begin has refused to bow to the protests, the Israeli press is pursuing the story with unrestrained zeal. New reports suggesting complicity in the massacre by at least the Israeli Army continued to appear today.

The independent newspaper Haaretz, which is critical of the Begin government, today quoted an Israeli soldier from an elite unit stationed near the Shatila refugee area of Beirut as saying, "It would have been possible to stop the massacre in Shatila as early as Thursday night if they had acted on what I reported to my officers."

The soldier told the newspaper that at dusk on Thursday, the day the Lebanese Christian militiamen entered the refugee camps with Israeli Army cooperation, he encountered "hysterical Palestinian women" running from the area screaming that the militiamen were shooting children and loading men on trucks.

"I told my officers, but they just said, 'It's okay,' " the soldier said. "My orders were to tell the women to go home, but a lot of women as well as entire families fled north from the camps."

He said he continued to report such instances, but each time was told, "It's okay."

The conservative newspaper Yediot Ahronot, a strong supporter of the government, reported yesterday that an officer of the Christian Phalangist militia had told Israeli officers that the militia's orders were to kill every male over the age of 12 in the refugee neighborhoods.

The newspaper said the Phalangist officer expressed surprise over Israel's shocked reaction to the massacre, remarking, "You still haven't learned what we've known for a long time. You must kill Palestinians while they are still small."

Such accounts, coupled with the admission yesterday by Sharon that the militia's entry to the camps was coordinated with Israeli officers and assisted after nightfall by the firing of flares by Israeli units, has made Sharon the object of the most intense criticism and the most frequent demands for his resignation.

At this point, however, only Begin could engineer Sharon's downfall and those who have long observed the prime minister think it unlikely that he would do that, out of loyalty to an associate and perhaps also out of self-interest.

Begin has said in recent private conversations about Sharon's possible ouster, "You don't run a party or a government by disloyalty to friends."

Moreover, although Sharon and Begin have never been particularly close, during recent months the two men have become inextricably entwined as the twin prime-movers in the Israeli drive to destroy the Palestine Liberation Organization. By now there may be no escaping from each other.

"If Sharon goes, I think Begin will go with him," said one Israeli journalist.

Whether Begin and Sharon together weather the storm appears to depend largely on how much pressure others in the country can generate in the coming weeks. Since 1977, Begin has dominated Israel as only founding father David Ben Gurion had been able to. But, despite Begin's considerable political and personal skill, much of his strength seems rooted in the weakness of others.

The main opposition Labor Party, political observers say, seems incapable of mounting an effective challenge to Begin. A Palestinian resident of Jerusalem, discussing the prospects for a change in governments in order to make progress in the negotiations over the occupied West Bank, remarked, "If the Americans are looking to the Labor Party to do it, they can forget it."

Within Begin's government coalition, a well-placed source said there are at least six ministers who are deeply disturbed by the massacre and are convinced that the government must make a more open response. But, with the exceptions of Energy Minister Yitzhak Berman and West Bank administrator Menachem Milson, who resigned their posts yesterday, none of them has yet made a move against the prime minister.

"They're afraid of Begin," the source said. "He's their mealticket."

To Begin, according to those who have talked to him recently, the whole uproar is nothing more than a political ploy by his opponents to topple the government. But deep inside him, suggested an Israeli who knows the prime minister well, there may be another reason for his refusal to consider any Israeli responsibility for the massacre.

In 1948, in a small Arab village named Deir Yassin, there was another massacre of Palestinians, about 240 of them, many of them women and children. It was carried out by members of the Stern Gang and the Irgun, an underground Jewish militia commanded by a future prime minister, Menachem Begin.

The Israeli added: "Ever since then, Begin has been tagged with this thing: terrorist, Arab-killer. Here he is, he's made peace with Egypt, won the Nobel Peace Prize, become prime minister of Israel. But he's embroiled in another Deir Yassin."