Prime Minister Menachem Begin, bending under intense domestic pressure, agreed today to ask the president of Israel's supreme court to investigate Israel's role in the massacre of Palestinian refugees in West Beirut. But a few hours later the judge turned down the job, at least for now, throwing the increasingly divisive issue back to the government.

The decision was made at an unusually brief emergency Cabinet meeting amid fresh disclosures that the Israeli Army received reports as early as last Thursday night that "300 civilians and terrorists" had already been killed in one of the refugee centers.

There were signs that the Begin government was beginning to crack under the onslaught of such disclosures and the mounting criticism following the massacre.

Shortly after receiving the request, the supreme court president, Yitzhak Kahan, said he could not comply immediately. Kahan said the court already had before it two separate demands for the convening of a State Judicial Board of Inquiry, the highest and most powerful investigative panel allowed under Israeli law, on the same matter. He said it would be improper for him to accept the Cabinet assignment while those cases are pending.

It is the convening of just such a board of inquiry -- which has subpoena powers and is the type that investigated the Israeli military and intelligence failures in the 1973 war -- that Begin appears determined to prevent. His gesture today to ask Kahan to investigate the massacre as an alternative seemed to satisfy a rebellious group of his own Cabinet ministers, some of whom reportedly had threatened to resign if the government did not authorize some kind of probe.

But even before the supreme court president turned down the request, it was clear that today's Cabinet decision would not satisfy opposition political leaders who are pressing ahead with plans for a mass protest rally in Tel Aviv Saturday night. Some organizers are predicting it could number in the hundreds of thousands and be the largest in Israel's history.

Kahan's refusal to conduct a probe was based on the fact that the Israeli Bar Association and the centrist Shenui Party already had filed requests for a State Judicial Board of Inquiry.

His action threw the Begin government back into a corner. Some ministers reportedly now are ready to demand that Begin accede to the powerful board of inquiry at the Cabinet's next meeting, now scheduled for Tuesday following the Yom Kippur holy day observances here.

The extent of the turmoil all this has caused within the Begin government was indicated today by the disclosure that Zeev Chafets, the director of the government press office and one of Begin's staunchest defenders, has asked for an extended leave of absence from his post. Chafets gave his reason as a desire to write a book, but he is known to be thoroughly disillusioned by Begin's refusal to accept any responsibility for the massacre.

The disclosure of Chafets' decision to leave the government came on the heels of the announcement early this morning that the commander of the Israeli Army Staff College, Gen. Amram Mitzna, has asked to be relieved of his duties because of the massacre.

The continuing uproar almost completely overshadowed the arrival in Israel last night of U.S. special envoy Philip C. Habib. He met with Begin, Defense Minister Ariel Sharon and Foreign Minister Yitzhak Shamir before today's Cabinet meeting to press the American demand for a complete withdrawal of Israeli forces from Beirut.

Israeli troops are expected to be largely evacuated from West Beirut by Sunday, but the Begin government has yet to make a commitment for a total withdrawal from the city.

Meanwhile, fresh indications of Israeli complicity in the massacre appeared today on the front page of the Jerusalem Post. The newspaper's military correspondent, Hirsh Goodman, reported that at 11 p.m. on Thursday, Sept. 16, the first night of the mass killings, the Israeli Army commander in Beirut was informed by the commander of the Christian Phalangist militia inside the Shatila refugee center that "up to now, 300 civilians and terrorists have been killed."

Goodman wrote that the message was immediately transmitted to Israeli Army headquarters in Beirut, where it was circulated among more than 20 officers and various bureaus. Noting that the message stated explicitly that civilians were being killed, Goodman said that such reports are normally transmitted to the offices of both the defense minister and Chief of Staff Rafael Eitan.

The rightist Christian militiamen remained inside the Shatila and Sabra refugee camps until the morning of Sept. 18, some 36 hours after the report allegedly was received by Israeli military commanders. Sharon and Eitan have acknowledged that the Phalangist entry into the refugee areas was coordinated with the Israeli Army, which assisted by firing flares over the neighborhoods at night.

But Sharon has insisted that it was not until the morning of Sept. 17 that Israeli Army officers heard the first vague "rumors" that civilians were being killed, a claim that would be directly contradicted by Goodman's report.

The Israeli military command said today it had no reaction to Goodman's account.

Israeli television said that its military correspondent Ron Ben Yishai told Sharon about the killings in a telephone conversation on the evening of the 17th, United Press International reported.

Sharon, in an interview on the television report, acknowledged that he had spoken to Ben Yishai but said that at the time he already had been told "that the operation had ended."

Similar reports are being carried daily in the Israeli press, greatly increasing the pressure on the Begin government. Today, for example, the afternoon newspaper Maariv reported that it was Eitan who met with Phalange militia officers on Sept. 17, when it was decided to allow the militiamen to remain in the refugee neighborhoods until the following morning.

On the night of the 17th, according to the same account, Sharon received a telephone call telling him that Israeli soldiers in the area had seen the militiamen "shooting children and other civilians."

The increasingly bitter nature of the controversy within Israel was exemplified by a confrontation today between Sharon and opposition Labor Party members in the parliament's Foreign Affairs and Defense Committee. After a stormy four hours of acrimonious exchanges, the Labor Party members stalked out of the closed meeting, charging that they had not been allowed to question Sharon about his role in the massacre.

Sharon reportedly spent most of the time renewing a charge he made earlier this week that Labor Party leader Shimon Peres, as defense minister, and party member Yitzhak Rabin, as prime minister, were partly responsible for an earlier massacre of Palestinian refugees by Phalangist forces at the Tal Zaatar refugee camp.

In public, Sharon has provided no evidence to back up this charge, which he also made in the public Knesset debate on Wednesday. It has been vehemently denied by Peres and Rabin.

Tal Zaatar was a Palestinian refugee camp in Beirut that rightist Christian forces besieged for 51 days, ending with its fall on Aug. 12, 1976, with the loss of hundreds of Palestinian lives. There were widespread reports at the time that Israel was supplying weapons to the Christian militiamen and also blockading the Lebanese coast to prevent weapons from reaching the defending forces in Tal Zaatar.

Sharon appeared yesterday at a memorial service for fallen Israeli paratroopers at which some people screamed "monster" at him. In his speech at the service, he charged that the condemnation of Israel over the massacre was part of a deliberate campaign to force Israel to surrender the occupied West Bank and Gaza Strip.

"I say, if we erred, if we assessed incorrectly, we will not hide a thing," Sharon said. "The subject will be investigated thoroughly, but in the face of all the hatred from abroad, there must be courageous unity. This is the moment in which we should transcend the internal debate -- which is legitimate and has a right to continue -- and stand together with all our strength and face the outside."

Sharon, reportedly shaken by the taunts of some in the crowd, met last night with Begin and is said then to have called for an investigation into the massacre.