Mounting indignation against Israel's role in the events surrounding last weekend's massacre of Palestinian civilians in Beirut swept through Congress yesterday, as members called for the resignation of Prime Minister Menachem Begin and questioned whether the United States should continue to increase military aid to the Jewish state.

At the same time, three of the most influential American-Jewish organizations -- B'nai B'rith International, the American Jewish Committee and the American Jewish Congress -- called for the Israeli government to launch an independent investigation into the circumstances of the massacre.

These expressions of disquiet came as the Reagan administration, seeking to look beyond the horror of Beirut and give renewed momentum to its Mideast peace initiative, was trying to cool off its dispute with Begin. However, the continuing domestic furor was a sign that the massacre has cast a shadow over U.S-Israeli relations that will be hard to dispel.

Even Sen. Alan Cranston (D-Calif.), long a bulwark of pro-Israeli support on Capitol Hill, called a news conference to release a four-page letter to Begin urging Israeli withdrawal from West Beirut. His letter said in part:

"You assumed responsibility for preserving order and protecting human life in Beirut -- in this you failed. It increasingly appears that you and Israeli Defense Minister Ariel Sharon have substituted naked military force for a balanced foreign policy which should reflect a decent respect for the opinion of mankind.

"Perhaps the most somber consequence of the current strife in Lebanon is the dimming of the inspiring moral beacon which has shone so brightly from beleaguered Israel."

Matching the unease of a longtime Israel supporter such as Cranston were the signs of growing unhappiness among American Jews over Begin's action in fighting and defeating a move in the Israeli parliament to set up an independent commission of inquiry into the massacre.

B'nai B'rith International, the 700,000-member Jewish service organization, labeled the killings a "heinous crime" and called for a "thorough and impartial" investigation by a panel of distinguished jurists "whose conclusions will be accepted and honored not only by their countrymen but by fair-minded people around the world."

The American Jewish Committee and the American Jewish Congress, both organizations long active in representing Jewish views on the American political scene, issued a joint call for an independent commission and added: "We believe that Israel owes this to itself and the civilized world."

These public statements followed private meetings at the Israeli Embassy here on Monday when representatives of a broad array of Jewish organizations told embassy officials that such an inquiry was essential, sources familiar with the meetings said. The statements issued yesterday appeared to mirror the arguments reportedly put to embassy officials at that time.

The signs of clear differences between the Begin government and important segments of American Jewry were accompanied by the growing drumfire of criticism directed against Begin from Capitol Hill.

Sen. Barry Goldwater (R-Ariz.), noting that he is half-Jewish, asserted that the United States had not armed Israel to allow it to become an aggressive nation. Begin, he said, "is a menace to the future of Israel . . . . Sometimes I think he can make Palestine Liberation Organization Chairman Yasser Arafat look like a first-class Boy Scout."

Sen. Jesse Helms (R-N.C.), a leader of the Senate's hard-core conservatives, said it would be "beneficial" if Begin resigned. "Prime Minister Begin has done the impossible," Helms charged. "He has almost made Yasser Arafat palatable to the American people."

Helms also warned that the American public will demand that weapons sales to Israel be halted "if there is not a cessation of the slaughter."

Sen. Paul E. Tsongas (D-Mass.), a leading spokesman for the liberal side of the chamber, said his colleagues had received massive amounts of mail following the massacre and that much of it was "very strongly anti-Israel." Sen. Joseph R. Biden Jr. (D-Del.), another normally strong supporter of Israel, added that there is "a lot of talk in the corridors" about using U.S. aid to force Israel out of Lebanon.

Despite such rhetoric, there seemed to be little support for actually reducing aid. The House yesterday passed a "continuing resolution" to fund the U.S. government at 1982 levels, and that includes a $2.1 billion appropriation for Israel. In addition, the bill made an exception to the normal funding formula to specifically give Israel $310 million more in direct grants -- as opposed to loans -- than it would have received under President Reagan's request.

Only Rep. Paul N. McCloskey Jr. (R-Calif.), a frequent critic of Israel, objected. Charging that the United States continues to send arms to Israel in violation of the agreement that they be used only in self-defense, he said that "continuing to send military supplies makes the United States complicitous in the massacre."

McCloskey contended that 40 of "the maddest congressmen I've ever seen" attended a State Department briefing on Lebanon yesterday, but that afterward one of them said that no one would fight the aid package because "we're running for reelection in November."

McCloskey added: "No matter what the rage, Congress is never going to take on the Jewish lobby before an election. Until Jewish leaders and AIPAC the American Israel Public Affairs Committee, which is the principal congressional lobbying arm of Jewish organizations speak out against Begin, Congress will never speak up."

The continuing resolution now goes to the Senate, where the uproar over the massacre has raised questions about whether the upper chamber will approve the Foreign Relations Committee's action in setting far more generous direct-grant terms for Israel than the administration had requested.

"There's increasing sentiment to hold to the administration's budget on aid for Israel , which still provides a 29 percent increase," said Sen. Richard G. Lugar (R-Ind.). In an echo of Biden's comment, Sen. John W. Warner (R-Va.) said that Israeli aid is "a subject under active discussion in the hallways."

These rumblings were in marked contrast to the increasingly soft tone taken by the White House and the State Department as the administration backed away from the angry language used by Reagan and other senior officials in the immediate aftermath of the massacre.

White House spokesman Larry Speakes, in what appeared to be an effort to disassociate the administration from the calls for Begin and Sharon to step down, sidestepped questions about Sharon's charge, during yesterday's stormy session in the Israeli Knesset, "that the Americans, too, want me to resign . . . . "

"It's up to the Israeli electorate," Speakes said as he characterized such questions as Israeli "internal matters."

Speakes and State Department spokesman John Hughes, in another sign that the administration has opted for persuasion rather than public criticism and pressure, both noted that Israel appeared to be thinning out its forces in West Beirut, and expressed cautious optimism that a withdrawal will follow.

Administration sources said privately that the quieter tone had been adopted deliberately to avoid an open break with Begin. That, they argued, would only have the effect of impeding further progress on getting Israeli and Syrian forces out of Lebanon and then moving ahead on wider efforts toward Middle East peace as envisoned by Reagan's initiative.

Despite continuing anger at Begin and distrust of his motives, the sources said, the president and his top advisers think that these are the main priorities for U.S. policy. They said the president's earlier tough talk has been noted by Israeli leaders, who now seem to be responding in a conciliatory manner by agreeing to redeployment of American, French and Italian forces in Beirut.

In addition, these sources continued, the administration is reasonably optimistic that Israeli troops will pull out of West Beirut by the time the multinational force arrives, probably over the weekend, and that a start can then be made on negotiating a wider withdrawal of Israeli and Syrian forces from all of Lebanon.

Meanwhile, the Defense and State departments were working out the precise role that the estimated 800 to 900 American Marines will play in Beirut. According to various sources, State wants as much flexibility as possible, while Defense Secretary Caspar W. Weinberger, aware of the potential for casualties, wants to use the force in the most prudent way possible.

In any case, the sources stressed, the Marines will in no way act as a police force. Instead, they said, the troops are intended to serve as a visible presence to provide a sense of security to Beirut residents frightened by the massacre and the continuing tensions between Moslem and Christian forces there.