Veteran diplomat Philip C. Habib met with Jordan's King Hussein in Amman yesterday as a special envoy of President Reagan as part of an unannounced U.S. effort to restart the Middle East peace process.

Habib's mission, confirmed by the State Department after it was disclosed in a bare-bones dispatch by the official Jordanian news agency, came after nearly two months of violence in the Israeli-occupied territories and after intensive Washington discussions in recent days with Egyptian President Hosni Mubarak and representatives of Israel's rival government leaders, Prime Minister Yitzhak Shamir and Foreign Minister Shimon Peres.

State Department officials said Habib's objective was to bring Hussein into the process as Secretary of State George P. Shultz tries a new tack in diplomatic explorations of the future of the strife-torn West Bank and Gaza strip.

"The United States has decided it can't consider 1988 as a dead year in Middle East diplomacy. My impression is it is about to enter a very active phase," said a foreign official who conferred with Shultz last week. Shultz selected the just-completed Mubarak state visit to Washington as "the jumping-off point" of a new diplomatic initiative, the official added.

Shultz's inclination, according to remarkably similar accounts from the foreign official and Shultz's senior aides, is to explore transitional arrangements to improve the living conditions and increase self-government and freedom for the Palestinians living in the West Bank and Gaza as well as to explore the territories' final political and legal status at the end of an interim period.

These issues were addressed in depth under U.S. leadership following the 1978 Camp David accords in the late stages of the Carter administration, but no agreements were reached. In the past several years, Middle East diplomacy was diverted to procedural questions, such as whether and how to organize an international peace conference as the forum for Arab-Israeli negotiations.

The State Department sources said Shultz has now concluded that the dispute over an international peace conference is so intractable that focusing on such procedural issues alone will simply perpetuate the deadlock at a time when the West Bank and Gaza disorders have generated demands on all sides for positive movement toward peace.

"We've got to work on both substance and procedures" of Arab- Israeli negotiations, said a senior official. He said Habib's charter was to discuss both sets of issues with Hussein in Amman, as Shultz and others here did earlier with Egypt's Mubarak during his state visit last week, Israeli Likud-bloc Cabinet Secretary Elyakim Rubinstein (from Shamir's side of the coalition) and Israeli Foreign Ministry Director General Yosi Beilin and former Israeli ambassador to the United States Simcha Dinitz (from Peres' side of the coalition).

Shultz also met last week on a less extensive basis with two West Bank Palestinian leaders, Hanna Siniora and Fayez Abu Rahmeh.

Habib, a retired undersecretary of state, was special U.S. Middle East negotiator from mid-1981 to mid-1983, during which time he was largely consumed by Lebanon issues. A consultant to the Bechtel Corp., where Shultz was president before becoming secretary of state, Habib is considered particularly close to Shultz.

State Department officials said they had no substantive report from Habib following his meeting with Hussein, but that a full-scale debriefing session is planned for Monday, when Habib is to be back in Washington. He was accompanied by two other senior officials, Deputy Assistant Secretary of State William A. Kirby and Dennis Ross, deputy chief of the Middle East office of the National Security Council staff.

Hussein, who ruled the occupied territories until they were captured by Israel in the 1967 war and who continues to have many ties in the West Bank and Gaza, is considered a crucial figure in any negotiated solution to the Palestinian question.

After seeking unsuccessfully to work out an agreed negotiating position with the Palestine Liberation Organization in 1983, Hussein quarreled bitterly with PLO leadership and only recently has begun to repair relations.

The same events, as well as affronts from Congress on arms sales and differences on the peace process, strained Hussein's ties with Washington. In an interview with Washington Post correspondent Jonathan Randal in Amman last Wednesday, Hussein expressed "pain, anguish and discouragement" over the United States.

Hussein is reported to have rejected a recent confidential appeal from Israel's Prime Minister Shamir to start autonomy talks for the occupied territories on the basis of the Camp David accords. Hussein reportedly also has had recent confidential correspondence with Mubarak on peace issues.Staff writer John M. Goshko contributed to this report.