President Reagan dispatched special U.S. envoy Philip C. Habib on a tour of Middle East capitals yesterday, signaling the start of a new phase in the drive for a negotiated withdrawal of Palestinian guerrillas from west Beirut.

Administration spokesmen said Habib's objective in travels to Syria, Saudi Arabia, Israel, Egypt and perhaps other countries will be to "explore further the ideas and understandings" which emerged in this week's Washington meeting with two Arab League emissaries.

The main development in the Washington talks, according to informed sources, was a suggestion by Saudi Arabian Foreign Minister Saud Faisal and Syrian Foreign Minister Abdal Halim Khaddam of a phased withdrawal of the Palestine Liberation Organization fighters. They would be evacuated from Beirut to Northern Lebanon in the first phase and be taken outside of Lebanon to several Arab countries in the second phase.

The Arab League ideas, at this stage, are considered by Washington officials to be preliminary, without enough detail or commitments regarding the proposed transfers to satisfy either Lebanon or Israel.

Nevetheless, it is clear that, at this point, the main U.S. hopes for a peaceful settlement to the showdown between Israel and the PLO forces are riding on the "constructive suggestions," as officials are calling them, made by Saud and Khaddam Monday to Secretary of State George P. Shultz and Tuesday to Reagan.

The departure of Habib from Beirut is an implicit recognition that negotiations there between the Lebanese government and the PLO, with Habib looking on from the wings, are likely to be inactive in the immediate future. Thus the focus of diplomatic attention and policymaking is shifting from Beirut to the surrounding capitals of the Arab world and Israel.

Habib's immediate objectives, according to Washington sources, will be to "crystallize" an Arab sense of responsibility for the future of the PLO fighters and encourage the Arabs to agree on the definite details and commitments that could make the phased withdrawal plan acceptable to all parties, especially Lebanon and Israel.

Despite the initially negative reaction from the Lebanese and Israeli governments, reactions which were anticipated here, "nothing is foreclosed," in the U.S. official view.

Administration officials viewed with concern the renewed Israeli military action yesterday against Syrian and Palestinian forces. But they described it as "a limited response" to Syrian and Palestinian activity, and expressed the view that it would not destroy the chances for a political settlement.

Despite the relatively optimistic tone of a White House briefing Tuesday on the meeting between Reagan and the two Arab emissaries, widespread doubts about the acceptability of the phased withdrawal ideas have endangered the credibility of Habib's effort to work out a negotiated settlement of the west Beirut showdown. Habib's travel may help to keep alive the hope that something can be worked out.

An expected meeting of the foreign ministers of the PLO and five Arab countries next week is likely to provide the first indication of the chances that the Arab League ideas can be made tangible and definite enough to have a chance of broad acceptance. A general meeting of Arab League foreign ministers or even an Arab summit may follow if progress is being made.

Saud and other Arab diplomats said a good deal depends on the willingness of the United States to give support for Palestinian rights, especially that of self-determination. This would imply backing for a Palestinian homeland, which the Arabs would then describe as the ultimate destination of the PLO.

State Department spokesman Dean Fischer said yesterday that "we will remain actively involved in the search for a resolution of the Palestinian problem in all its aspects, beginning with the resumption of the autonomy talks at the appropriate time."

Fischer also denied a press report that Habib had asked for authority to negotiate directly with the PLO, and reiterated once again the standard and unchanged U.S. position on prohibiting U.S. officials from having contacts with PLO officials until the PLO recognizes the right of Israel to exist.