President Reagan has sent a secret letter to Syrian President Hafez Assad offering to improve relations after a period of strain between the two countries, administration officials said last night.

The State Department confirmed the existence of the letter after John McWethy of ABC News reported that Reagan had offered in the message to send a special envoy to Damascus to open a high-level discussion, and that Assad had accepted the offer.

Official sources said last night the Reagan letter, which was sent to Damascus late last week, resulted from deliberations that had been taking place within the administration since early last month about improved U.S. relations with Syria.

Washington recalled its ambassador to Damascus, William L. Eagleton Jr., last Oct. 24 as a protest against Syria's alleged complicity in an attempt to bomb an Israeli jetliner at London's Heathrow Airport on April 17, 1986. The British government broke diplomatic relations with Syria over the incident.

Officials said the administration, while concluding that Syria's record on international terrorism had greatly improved since last fall, promised British Prime Minister Margaret Thatcher that it would not take steps to improve relations with Syria before the June 11 British election. This was because Thatcher was concerned that such a U.S. move could be seen by the British voters as evidence of friction between the two governments.

Informed sources said the letter to Assad was in final stages of preparation when U.S. journalist Charles Glass was kidnaped June 17 by a pro-Iranian group operating in a Syrian-controlled area of Beirut. The sources said a reference to the Glass case was inserted in the letter to Syria, which has exerted strong efforts to obtain his release. Officials said, however, the Glass case was not the motivating factor behind or the main point of the letter.

A U.S. official said that terrorism and hostages were discussed in the letter to Assad, along with other aspects of Syria's role in the Middle East, including the Persian Gulf war between Iran and Iraq and the

Arab-Israeli peace process.

Syria, which has been an ally of Iran during most of the nearly seven years of the Iran-Iraq war, is reported to have been shifting its position in recent weeks. Press reports here and in the Middle East said that Assad met in late April with Iraqi President Saddam Hussein, who was previously a bitter enemy.

Reports from Jordan early this month said Syria has closed down the offices of Palestinian terrorist Abu Nidal. Still other reports suggested that Syria is ready to participate in an international peace conference for the Middle East that would be an umbrella for talks between Israel and its Arab neighbors.