The United States sent another strong signal yesterday that it wants to improve relations with Syria, virtually asking Damascus to invite Assistant Secretary of State Richard W. Murphy to visit there during his mid-April swing through the Middle East to discuss new Arab proposals for reviving the peace process.

State Department spokesman Ed Djerejian, reading a prepared statement, said Murphy "would welcome another opportunity" to consult with Syrian officials. He made a point of saying that no itinerary had been fixed for his trip to discuss new Arab proposals for reviving the peace process.

He went on to say that the United States has maintained "a high-level dialogue" with Syria on the peace process in the past, and that it hoped "to continue and intensify" it.

"While there are obvious differences between our position on the peace process and that held by Syria, the United States is committed to supporting movement toward peace between Israel and all its Arab neighbors," he said.

"Our consistent goal has been to bring about direct negotiations between Israel and all its Arab neighbors, including Syria, on the basis of United Nations Security Council Resolution s 242 and 338.

Behind the statement stands a clear awareness that Washington is mindful of the dangers involved in attempting to renew peace talks in the face of strong Syrian opposition to proposals by King Hussein of Jordan and President Hosni Mubarak of Egypt.

The Jordanian and Egyptian proposals are aimed at getting both Palestine Liberation Organization chief Yasser Arafat and the United States involved in a new a round of negotiations, together with Jordan and Egypt, through a joint Jordan-Palestinian delegation.

Syria strongly opposes the new proposals, and opposes recognizing Arafat as PLO leader, apparently because there is no role for Syria in the talks, and because the main focus would be on the Palestinian issue and not the Israeli-occupied Syrian Golan Heights.

Whether a new round of peace talks faced with stiff Syrian opposition would have any chance of success with stiff Syrian opposition remains unclear. But U.S. policy-makers are aware that Syria singlehandedly overturned the U.S.-brokered Lebanese-Israeli agreement of May 17, 1983.

This largely explains the new conciliatory attitude by the United States toward Syria and its leader, Hafez Assad, whose attitude toward the whole peace process remains ambiguous.

Since mid-February, Washington has been courting Assad with a series of statements calculated to convince him that the United States is not trying to keep him isolated from the peace process and also is interested in the fate of the Golan Heights.

In addition, after the U.S. television reporter Jeremy Levin escaped from his Shiite extremist captors in Lebanon Feb. 13, President Reagan called Assad to thank him for his help, although there was no indication that Syrian security forces had played any role in the release.

The Syrian leader had been helpful, however, in trying to locate Levin, according to State Department officials. He also was instrumental in gaining the release in July 1983 of David Dodge, former acting president of the American University of Beirut.