The United States and Lebanon have begun work on a new diplomatic attempt to break the deadlock encountered by Secretary of State George P. Shultz on his recent Middle East trip, Lebanese Foreign Minister Elie Salem said yesterday.

Salem, who conferred with Shultz for more than an hour at the State Department, said afterward that U.S. and Lebanese diplomatic teams will engage in detailed discussions here Monday and Tuesday on "specific points" to be presented to Syria and Israel as well as moderate Arab nations in the quest for withdrawal soon of all foreign forces from Lebanon.

Among the ideas being considered, Salem suggested, are ways to assure Syria that its security will be protected after its troops are withdrawn. If Damascus can be persuaded that tangible gains have been made, he said, it may be willing to reverse course and move toward withdrawal without formally accepting the recently negotiated Israeli-Lebanese pact.

The initial discussions here will set the stage for meetings Thursday and Friday between Lebanese President Amin Gemayel and top U.S. officials, including Shultz and President Reagan, aimed at producing "a timetable for action or for testing ideas within a very short period" through presentation to other Middle Eastern parties, Salem said.

A Washington visit next week by Israeli Prime Minister Menachem Begin will provide an occasion for presenting new options to the Jewish state.

Salem held out the possibility of a renewal of U.S.-Syrian discussions within the next few weeks, despite the stone wall that Shultz encountered in his five-hour session with President Hafez Assad in Damascus on July 6. "I think it is in the interest of both Syria and the United States to have a continuing dialogue," he said.

"We have a great sense of urgency. Our economy is threatened because of the stalemate. There is danger of demoralization of our population . . . . There is danger of losing the national consensus," said Salem, who arrived in Washington amid reports of renewed fighting between ethnic and religious groups in battle-scarred Lebanon.

U.S. credibility in the Middle East and the validity of its commitments are at stake in the present phase of Lebanon's travail, according to Salem. As tangible evidence of the commitment, 1,800 U.S. Marines are stationed in Beirut indefinitely, as part of a multinational peace-keeping force.

"For us time is of the essence," Salem said. "We cannot afford to say the month of August is the month of vacation when things are at a standstill and the next meeting will be in September when the United Nations meets and the foreign ministers come to New York. We cannot think like that at all . . . .

"We do not mind if one idea fails and then we try another. We do not mind if the process continues more than a month or two or three or four, provided all the time you are testing credible ideas, you are pursuing them and you are not just waiting for Godot."

At present, he said, a major problem is the "very close" alliance of Syria with the Soviet Union, which he described as "determined to foil American plans in Lebanon or any Middle East plan in which they are not a part."

Salem also said that Syria has fears about the Israeli-Lebanese agreement, believing that it "brings in the American presence to Lebanon" and "converts a big part of Lebanon into an Israeli protectorate."

Regarding Israel, Salem amplified his government's position on a partial withdrawal or redeployment of Israeli forces to more easily defended lines. Israel has refused to withdraw totally from Lebanon until Syria does the same, but is considering a limited pullback.

"We do not want to be a party to any discussion on a partial withdrawal" of Israeli forces that is not an integral step in a total withdrawal, Salem said. At the same time, however, he seemed to indicate that Beirut would accept such a limited pullout, describing it as a "sovereign decision" for Israel to make and saying, "if they do withdraw on their own, we are ready immediately to send the Lebanese army. And we expect to have multinational support in that."

Lebanon is concerned, he said, that any limited Israeli pullout could be "a time bomb" that could provide a pretext for Israel to return in case of trouble.

He said that his government is also "quite concerned" about how to explain such a redeployment to those in Lebanon who see it as a step toward "a small Lebanon," with Israel holding some areas and Syria others, all with U.S. acquiescence.