Prime Minister Menachem Begin yesterday tacitly rejected President Reagan's call for a pullback of Israeli forces in West Beirut. But, despite that disappointment and the outbreak of new fighting in Beirut, U.S. officials continued to express hope that a negotiated settlement of the Lebanon crisis can be achieved.

Begin's formal reply to the appeal Reagan made Wednesday was delivered to Secretary of State George P. Shultz yesterday by Israeli Ambassador Moshe Arens. Although U.S. officials refused to discuss its contents, sources here and in Israel said it amounted to a refusal to ease the siege of Beirut in ways that the United States considers vital to the negotiating process.

Specifically, Reagan had asked Israel to surrender the gains it made in fighting this week and to withdraw to the positions it held last Sunday. The president also sought assurances that Israel would refrain from further attacks on the city for a time sufficient to enable Reagan's special envoy, Philip C. Habib, to pursue an agreement for the departure of Palestine Liberation Organization forces from Lebanon.

In a clear reflection of the strain that the Lebanon situation has put on U.S.-Israeli relations, Begin pointedly addressed his letter to "The President of the United States, Ronald Reagan," rather than using the "Dear Ron" salutation customary in past correspondence between the two.

According to the sources, Begin's letter, while not referring directly to Reagan's request, rejected the idea of a pullback. Instead, it repeated the position enunciated by the Israeli Cabinet Thursday night that "arrangements for the deployment of Israeli forces will be determined following the departure of the terrorist organizations" from Lebanon.

In regard to Reagan's call for restraint, Begin said Israel will continue to respond to Palestinian cease-fire violations as it sees fit. While reiterating his hope that Habib can achieve a peaceful solution, the prime minister reportedly complained that Habib has made no progress in almost seven weeks of negotiation; and he intimated that complaints about Habib's efforts being hindered by constant cease-fire violations should be addressed to the PLO rather than Israel.

Despite the uncompromising tone of Begin's response, U.S. officials said they were not inclined to read it as the epitaph for the Habib mission. Of greater interest to the United States at this point, the officials continued, is whether Israeli actions, as opposed to words, display sufficient restraint in the days ahead to permit Habib some breathing space for his efforts.

The officials said the administration believes the work done by Habib in the past two days has given some increased grounds for optimism, and they added that the United States will continue to try and afford him the maximum possible protection against new interruptions.

On Thursday, administration sources said that Habib has been stymied repeatedly by outbreaks of fighting that bring negotiations to a halt and create new tensions. The administration, they said, had hoped to win from Israel a period of roughly two weeks in which there would be no fighting while Habib made a final test of whether a plan to evacuate the PLO to other Arab countries could be agreed upon and carried out.

In the light of Begin's reply, U.S. officials conceded yesterday, it does not seem likely that Habib can count on a grace period of that duration, or that the United States will be able to offer an Israeli pullback as proof to the PLO of American evenhandedness in the negotiations.

But, they stressed, there still is considerable latitude for Israel to help the negotiating process through restraint. While it will take a few days to determine the degree of Israeli cooperation, the officials said they believe Begin is as eager as Reagan to avert a confrontation; and they expressed hope that it will be possible to avoid a return to the talk of sanctions and other threats that surfaced earlier in the week.

The officials said that the flare-up of fighting in Beirut yesterday, while nasty, did not warrant the description in some initial news reports of a "major thrust" by Israel against the PLO. Instead, they added, the evaluation of the U.S. Embassy in Beirut was that the major fighting resulted from Israeli forces striking back against Palestinian fire; and they said the United States did not regard it as an attempt to reinforce Begin's letter with a gesture of defiance on the ground in Beirut.

The administration also denied suggestions that the United States, in spite of its public opposition, privately supports Israel's military pressure on Beirut.

State Department spokesman Alan Romberg said, "The reality of a continued Israeli military presence around West Beirut is, we believe, a clear form of pressure," and he noted that, unless a diplomatic settlement is reached soon, "there is a real danger of military action" by Israel.

But, Romberg added, while that view was expressed on Thursday to American Jewish leaders during a meeting with senior administration officials, it was intended as a statement of reality and not as an endorsement of Israeli tactics.

"We have made it clear that we are opposed to military action which results in the loss of innocent civilian lives and sets back the prospects for a successful negotiation," Romberg said. "The prospects of success in our negotiating efforts are best enhanced by a stable cease-fire."