Washington — Judging by the public statements of many American Jewish leaders, one might think that the American Jewish community totally supported the Israeli invasion of Lebanon.
But it is clear that a number of American Jews, and that certainly includes some leaders, are in anguish over what is happening in Lebanon.
They are concerned about reports of civilian casualties. And they are concerned that the Israeli thrust into Lebanon may be creating a tidal wave of reaction against Israel around the world. Because of a fear that Israel will be further isolated by this reaction, some feel a need, in their public posture at least, to rally behind Israel.
But if the Lebanon operation turns into a destructive battle for West Beirut, an increasing number of prominent American Jews can be expected to protest.
Already there are a few cracks showing in the unity of American Jews. Philip M. Klutznick, president emeritus of the World Jewish Congress and honorary president of B'nai B'rith International, has joined former French Premier Pierre Mendes-France and Nahum Goldmann, former president of the World Jewish Congress, in calling for a lifting of the siege of Beirut and Israeli negotiations with the Palestine Liberation Organization (PLO). In the view of the three Jewish elder statesman, such negotiations would be aimed at achieving a political settlement based on mutual recognition between the PLO and Israel.
The statement by the three, which was issued July 2 in Paris, was welcomed by Isam Sartawi, a PLO representative in Paris who is considered a moderate figure among Palestinians. But it was, predictably, denounced by leaders of major Jewish organizations in the United States.
Three executives of the Anti-Defamation League (ADL) of B'nai 'rith, the Jewish social service organization, said they did not regard the statement as helpful or realistic, partly because it ignores ''the failure of the PLO to abandon its official call for the destruction of Israel.''
Julius Berman, the new chairman of the Conference of Presidents of Major American Jewish Organizations, in speaking of Mssrs. Goldmann and Klutznick, said, ''I've never suggested that either Nahum or Phil has no right to speak out. But they represent themselves and only themselves. I feel that they are in less than a minority. They are overwhelmingly in the minority.''
Berman contends that his organization, which groups together the leaders of more than 30 Jewish organizations throughout the US, represents substantially more than the majority of American Jews.
When it comes to the Israeli move into Lebanon, he says: ''My feeling is that . . . the overwhelming consensus of the Jewish community in the United States is in support of the operation in Lebanon.
''We are also very supportive of the Reagan administration in its desire to help reconstitute a new government in Lebanon and to arrange for the evacuation of all foreign troops . . .''
Nathan Perlmutter, the national director of the ADL, said that while he believed that most American Jews were ''deeply anguished'' by the war and deaths in Lebanon, they were understanding of any Israeli move which aimed at removing a PLO threat to Israel.
Perlmutter also stated a theme often emphasized by Jewish leaders when he asserted that the PLO had ''purposively placed itself in civilian areas, waging its war from cynically selected civilian shelters.''
Barring radical changes in the PLO, few American Jews would be likely to go as far as Mssrs. Goldmann, Klutznick, and Mendes-France did in proposing the PLO as a negotiating partner. But it is clear that a number of rabbis as well as prominent Jewish intellectuals in the US - if not members of the Jewish rank and file - feel that Israel's Prime Minister Menachim Begin and Defense Minister Ariel Sharon have gone too far in their attack into Lebanon. Their distress came into the open during the course of debate at the annual convention of reform rabbis in New York on June 30. And it has been evident in the writing of intellectuals such as Harvard Professor Nathan Glazer, the co-editor of ''The Public Interest,'' Seymour Martin Lipset, a Stanford University professor who is president of the American Political Science Association, and Leonard Fein, editor of the Boston magazine ''Moment.''
Arthur Hertzberg, former president of the American Jewish Congress and a self-described ''dove'' in the Arab-Israeli conflict, summed up what he described as moderate Jewish opinion on Lebanon in this way: ''There is . . . a kind of two-edged anger: first, anger at Begin and Sharon for having overdone it. Second, anger at the press for using this as a holiday to beat up on Israel. . . .
''There is a feeling that this war has been quite expensive - in terms of casualties and in terms of moral credits lost . . .''
But Mr. Hertzberg disagreed with the proposal made last week in Paris for negotiations with the PLO, arguing instead that a new effort must be made to see that the Egyptian-Israeli negotiations over autonomy succeed. He said that the statement by Mssrs. Goldmann, Klotznick, Mendes-France, was ''counterproductive'' and had ''a tendency to polarize Jewish opinion.''