President Reagan, concerned by the lack of progress in the talks on foreign troop withdrawal from Lebanon, sent his special Middle East representative, Philip C. Habib, back to the region yesterday with instructions that Habib described as an attempt to "accelerate the process."

Talking with reporters before his departure, Habib refused to say whether the United States holds Israeli Prime Minister Menachem Begin primarily responsible for the impasse in the negotiations.

However, Habib's remarks, including the revelation that his first order of business will be to talk with Begin, left little doubt that the administration is chafing at Israel's insistence on discussing issues other than a pullback of its troops.

Following a White House meeting with Reagan and top administration policy-makers, Habib said the president is disappointed at failure to achieve withdrawal from Lebanon and regards the stalemate there as a barrier to movement on his broader Mideast peace initiative.

"There is an urgent need to put the problems of Lebanon behind us so that we can move on to the larger issues of peace in the region," Habib asserted. "These problems need to be dealt with on an urgent basis, and they can be dealt with."

The envoy said that, at this stage, he did not plan to join Reagan's Lebanon mediator, Morris Draper, at the current Israeli-Lebanese negotiating sessions but would begin his mission instead by talking with Begin.

He rejected the word "pressure" as applicable to the planned session with Begin and said, "Let's call it persuasion, good sense and a common objective."

Administration officials said privately that Habib is carrying a letter from Reagan underscoring to Begin the U.S. view that progress on withdrawal is urgently needed and that Israel should not press its demands for an agreement implying Lebanese recognition of the Jewish state.

Lebanon argues that to yield to Israeli pressure would isolate it from other Arab nations.

The United States, working through Draper, has suggested various compromises for breaking the logjam over what should be included in the agenda for the Lebanon talks.

The message being carried to Begin is understood to urge that Israel accept these compromises. While reliable sources said it is couched in positive terms, they added that it makes clear Reagan's impatience and thus hints that continued delay could lead to further worsening of U.S.-Israeli relations.

In addition to concern about the effects of a continued Israeli military presence on Lebanon's internal stability, the United States is fearful that, as long as Israeli troops remain in southern Lebanon, the Arab world will be constrained from responding favorably to the Reagan initiative's call for broadened peace talks to resolve the Arab-Israeli conflict.

During the next four to six weeks, Reagan is to be visited by Egyptian President Hosni Mubarak, Begin and possibly Jordan's King Hussein, whom the administration is trying to entice into the stalled Egyptian-Israeli talks on the future of the West Bank and Gaza Strip.

U.S. officials regard these impending talks as potentially decisive in determining whether the peace process can be broadened and revitalized. But they also are aware that the pressures of Arab-world politics will prevent Mubarak and Hussein from making overtures toward Israel while it continues a massive occupation of another Arab country.

Hussein visited Reagan before Christmas and is understood to have come under heavy U.S. pressure for a decision on his willingness to enter the peace talks. U.S. officials said yesterday that the king, concerned about being isolated, wants to strengthen his position by obtaining Saudi Arabia's public backing and at least tacit Palestine Liberation Organization approval to enter the process as representative of the Palestinian inhabitants of the occupied territories.

The Saudis' failure to come forward has strongly disappointed the administration and Hussein, who wants a Saudi endorsement to give his position legitimacy in the Arab world and help counter Syria's efforts to block progress on the U.S. proposals.

However, the officials said, delicate negotiations among Jordan, the PLO and Saudi Arabia continue and should be wound up within two weeks. Then, they added, a clearer picture should emerge of whether Hussein is gaining the support he regards as necessary to come closer to the bargaining table. In what sources described as an attempt to prepare the way for an eventual expanded peace process, the administration plans to name Wat T. Cluverius, a State Department special deputy for the Mideast negotiations, as consul general in Jerusalem. That post is the principal point of contact between the United States and West Bank Palestinians.

The State Department also expressed concern yesterday about recent incidents in which Israeli troops have approached the positions of U.S. Marines in the multinational peace-keeping force in Beirut. "We have made it clear that the zone of deployment of the MNF is closed to all military forces other than those of Lebanon and the MNF," department spokesman John Hughes said.

Also yesterday, Habib, Hughes and White House deputy press secretary Larry Speakes publicly praised the performances of Draper and Nicholas Veliotes, assistant secretary of state for Mideast affairs. They were responding to a published report that the White House is dissatisfied with their failure to achieve progress on Lebanon.