Ambassador Vernon Walters, as President Reagan's special envoy, met yesterday in Damascus with Syrian President Hafez Assad to discuss the Syrian attitude toward terrorism and explore an improvement in U.S.-Syrian relations.

Officials here characterized the Walters mission as the first step in renewing the high-level dialogue with Syria. Washington withdrew its ambassador to Syria last Oct. 24 to protest Syrian complicity in an attempt to bomb an Israeli jetliner at London's Heathrow Airport.

Walters, who is U.S. ambassador to the United Nations, spoke to reporters in Damascus shortly after State Department spokesman Charles Redman confirmed Syrian reports of the discussions. Walters said he and Assad had two meetings covering Mideast issues and bilateral questions.

Official sources in Washington said Walters was asking Assad to use his influence on behalf of U.S. and other foreign hostages being held by extremist groups in Lebanon. Walters was also reported to be discussing the Mideast peace process and a wide range of other regional issues with Assad, who is an important player in Mideast maneuvering on a variety of fronts.

The Associated Press quoted a Syrian spokesman in Damascus as saying the talks focused on "Middle East developments and issues" and "relations between Syria and the United States."

The Walters trip resulted from a letter Reagan sent to Assad in mid-June, after a period of strain between the two countries, offering to send a special envoy to Damascus. Assad approved the idea and Walters, who has had extensive experience as a high-level intermediary and who has previously met Assad, was selected for the task.

Reports that Syria recently closed the Damascus offices of the Abu Nidal terrorist group contributed to the U.S. decision to take the initiative in seeking an improvement in relations, according to officials.

Administration sources said they have no confirmation of a Cable News Network report from Damascus that Syria has learned the names of some of the kidnapers of American journalist Charles Glass and other hostages in Lebanon as well as the locations where some of the captives are being held.

The report, attributed to a "senior Syrian military source," said that Iran has been told "in the bluntest possible terms" to use its influence to free Glass and other hostages, and that Assad is considering a plan to intervene militarily if political efforts to free the hostages fail.

In a separate development, the State Department said Assistant Secretary of State Richard W. Murphy met in Geneva yesterday with Vladimir Polyakov, chief of the Soviet Foreign Ministry's Middle East department, to review U.S. and Soviet policies in the Mideast. A second meeting was scheduled today.