The Reagan administration is deeply frustrated over its inability to persuade Israeli Prime Minister Menachem Begin that his nation's military actions in Lebanon are damaging both U.S. and Israeli interests in the Middle East, according to well-placed administration sources.

Reagan administration officials predicted today that the American suspension of F16 fighter-bomber shipments to Israel, ordered Monday night by the President, could remain in effect for a considerable time unless it becomes clear that Begin genuinely intends to reduce the violence in Lebanon.

"It's not going to be easy to reverse what's been done," one official said. "This could be a watershed for U.S. policy with Israel."

Another official called the suspension "open-ended" and added: "What if we sent the planes and the Israelis the next day bombed the hell out of Beirut? At this point we have to have some sense that there's going to be something more permanent than a temporary cease-fire."

Publicly, neither Secretary of State Alexander M. Haig Jr. nor White House counselor Edwin Meese III would make any prediction about when shipments of F16s are likely to resume.

But what emerged from a series of private discussions with U.S. officials attending the seven-nation economic summit here was a picture of a policy being pushed by events in a different direction than both Reagan and Haig would like it to go.

One official said that the President was "truly troubled" by what he saw as the necessity of further delaying the shipment of the planes to Israel, which Reagan has supported since the creation of the Jewish state in 1948.

Another official said that Haig was "in anguish" over having to recommend this policy -- a policy in which all other high officials of the government concurred, including those who traditionally have been most supportive of Israel.

One official said he expected that American public opinion is swinging sharply against Israel because of its recent military actions, especially the bombing of Beirut last Friday that killed 300 civilians. The frequent polls taken for the White House on every important policy question are expected to demonstrate this change of sentiment.

However, the administration is not deriving comfort from the perception that Reagan's suspension of the F16 shipments may prove popular with Americans outside the Jewish community. Instead, the attitude here is one of frustration over the difficulty of communicating the depth of U.S. sentiments to Begin.

"It could be said that we've tried both the carrot and the stick, and that neither method has worked," a U.S. official said.

The frustration is all the deeper because of the reliance of other Western nations on U.S. ability to restrain Israel. For years, other countries have been urging the United States to take a harder line with its Middle East ally. Now that this has happened, there is no evidence that Israel is listening.

The atmosphere within the administration is not one of complete gloom. One official today took heart from the fact that Begin has so far responded to U.S. actions "more in sorrow than in anger." And Richard V. Allen, the president's national security adviser, said in reference to a wire service story from Israel that it was "a hopeful sign" that Begin is agreeable to considering a cease-fire, despite his refusal to deal directly with the Palestinians.

Despite these scraps of optimism, the wording used by Haig when he announced the President's decision Monday indicated that it is unlikely that any F16s will be shipped to Israel until the administration is convinced that the fighting on both sides has stopped for more than a temporary truce. Haig said Monday that Reagan had suspended the shipments because it would have been "highly inappropriate . . . to send additional armaments into the area while this level of violence continues and until the situation clarifies."

Israel already has received 53 of the 75 F16s it has ordered from the United States. Ten have been held up and another four are scheduled to be sent in mid-August. An administration official said he believed that Reagan's order Monday will apply to the four unless there is a "dramatic change" in the situation.

Campaigning for the presidency in 1980, Reagan frequently expressed the view that President Carter's policy in the Middle East was misguided. Reagan believed that Carter was unsympathetic to Israeli interests and did not fully understand how important Israel was to the security of the United States.

Now, Reagan finds himself having to take actions of the kind he surely would have criticized during the campaign.

As one American official put it, "We're walking a tightrope and it's not a comfortable position."