Syria has said it wants to work with the US to reimplement the 1974 disengagement agreement with Israel, which created a UN-patrolled buffer zone separating the two countries' forces.
During a phone call with US Secretary of State Marco Rubio, Foreign Minister Asaad Al Shibani expressed Syria's “aspiration to co-operate with the United States to return to the 1974 disengagement agreement”, the Syrian Foreign Ministry said in a statement.
Israel violated the agreement when its troops entered the zone after the rebel forces toppled Syrian president Bashar Al Assad in December.
Washington has been driving diplomatic efforts towards a normalisation deal between Syria and Israel, with US envoy Thomas Barrack saying last week that peace between the two was needed.
Speaking to The New York Times, Mr Barrack confirmed this week that Syria and Israel were engaging in “meaningful” US-brokered talks to end their conflict.
Israel launched hundreds of air strikes on military targets in Syria and carried out incursions deeper into the country's south after the overthrow of Mr Al Assad, whose regime survived nearly 14 years of civil war with the help of Iranian and Iran-backed forces.
Syria's new authorities refrained from responding to the Israeli attacks and admitted to holding indirect talks with Israel to reduce tensions.
The two countries have no official diplomatic relations, with Syria not recognising Israel and the two nations technically at war since 1948.
Israel conquered around two-thirds of the Golan Heights from Syria during the 1967 Arab-Israeli war, before annexing it in 1981 in a move not recognised by any country other than the United States.
A year after the 1973 war, the two reached an agreement on a disengagement line.
As part of the deal, an 80km-long United Nations-patrolled buffer zone was created to the east of Israeli-occupied territory, separating it from the Syrian-controlled side.
Israeli Foreign Minister Gideon Saar said on Monday that his country had an “interest” in normalising ties with Syria and neighbouring Lebanon.
He added, however, that the Golan Heights “will remain part of the State of Israel” under any future peace agreement.
Syrian state media reported on Wednesday that “statements concerning signing a peace agreement with the Israeli occupation at this time are considered premature”.
During the call with Mr Rubio, Mr Al Shibani received a formal invitation “to visit Washington as soon as possible”, the Syrian Foreign Ministry said on Friday.
It said the two men also discussed Syrian President Ahmad Al Shara's participation in the upcoming UN General Assembly.
Mr Al Shibani visited the UN headquarters in New York in April, where he raised Syria's new flag.
He and Mr Rubio also talked about “the Iranian threat in Syria”, with Damascus expressing “its growing concern over Iran's attempts to interfere in Syrian affairs, especially following the strikes that recently targeted Tehran”, the Foreign Ministry said, referring to last month's Israel-Iran war.