Masking their concerns with a public display of unity, the presidents of America's major Jewish groups met today with Israeli ambassador Ephraim Evron and applauded his assertion that Israel did the "only thing" it "could have don" in the bombing of residential Beirut.

But privately, some of the Jewish leaders said the Israeli bombing is causing considerable dismay among their members. Howard Squadron, chairman of the group, told them he was flying to Israel this evening to convey that concern personally to Prime Minister Menachem Begin.

Evron vigorously defended the Israeli actions. "Any government that has anyresponsibility . . . has to act to protect its citizens when they see the international community sitting by, doing nothing and saying nothing," Evron said to explain a raid that killed as estimated 300 persons in Lebanon in the process of destroying a Palestinian Liberation Organization headquarters.

Prior to today's meetings of the presidents of 37 of America's major Jewish organizations,a number of them expressed concern that Israel for the first time had conducted an attack that killed large numbers of civilians, much as it has accurately charged for years that Arab terrorists had done to Israelis. Some strongly questioned why Israel needed to conduct such a raid and expressed grave concerns that the greatest damage done by the raid may be the deterioration of American public support for Israel.

But before the meeting began, one prominent member of the group predicted, "We'll probably all take refuge in silence." And as reporters and cameras looked on, that is exactly what happened when Evron came to make his statement of defense.

However, after Evron left the meeting, and after the reporters were also asked to leave, some of these concerns were discussed in a closed session. According to Squadron, one of the organization presidents said in effect:

"I have heard great concern from people in my organization about the Beirut bombing. And we must deal with that concern."

At this point, Squadron said, he told his colleagues that he is flying to Israel tonight and will meet with Begin tomorrow.

Sources within the group said that a number of the leaders decided to wait until after they hear Squadron's report about Begin's response before deciding whether to take further public action or make further statements. The sources said that these leaders would like some assurance that Begin understands the depth of American concern over the raid on residential Beirut and some indication that Israel will confine its military operations to attacks on military installations.

The presidents of the Jewish organizations did take one significant public action today, sending a telegram to President Reagan urging "immediate resumption of F16 plane deliveries committed to Israel by our country."

Reagan suspended delivery of 10 F16s after the Beirut bombing. "The suspension of these shipments can only be viewed throughout the world as a one-sided punishment of Israel," the telegram said. "Denying American arms to Israel will encourage those committed to Israel's destruction to escalate their attacks against the Jewish state. It will embolden those in the Arab world who have denounced the Camp David agreements . . . and those in the Third World and elsewhere who have attempted to undermine the Camp David peace process."

In the meeting, the Jewish leaders listened in silence as Evron said, "It is natural that we did the only thing we could have or should have done" in ordering the bombing of the PLO headquarters in residential Beirut. He added, "We are determined to put an end" to the PLO attacks on villages in northern Israel.

"This was a very anguished decision to take," Evron said, "and no one regrets the deaths that followed more than we." He added that "we are not the first ones" to kill civilians in time of war, saying that U.S. efforts to destroy German rockets aimed at England resulted in the deaths of many civilians in Holland, Belgium and France in World War II.

Evron, who was applauded at the end of his presentation, said that the current status of U.S.-Israeli relations amounts to "differences of opinion between close friends." But he added, "We are not going through a crisis now."

However, another knowledgeable Israeli official privately took a different position in an interview. He said that it was important to "prevent any further deterioration in relations between the United States and Israel." Asked to characterize the relationship, he said, "It's bad." And he added:

"It's a tough hour between the two countries -- perhaps one of the toughest."