Syrian President Bashar al-Assad told visiting British members of parliament on Tuesday that progress on the Syrian-Israeli peace track would encourage Lebanon and Israel to initiate their own talks.
"The president hinted that it would not be in Lebanon's interest if it did not have its own talks if Syrian-Israeli talks advanced," the source familiar with the talks said.
Meanwhile, Syrian sources said on Wednesday that the talks would resume in the coming days.
Assad dismissed on Tuesday Israeli demands for Syria to abandon an alliance with Iran as a requirement for a peace deal.
The Syrian president told British MPs that the Baath Party government intended to maintain its "normal relations" with Iran while it conducts indirect talks with Israel to regain the occupied Golan Heights, a source familiar with the meeting told Reuters.
Israeli officials have repeatedly said that the peace agreement depends on Syria distancing itself from Iran, and severing ties with Lebanon's Hezbollah movement and Palestinian group Hamas. The two organizations are also supported by Iran.
"The president said Syria has normal relations with Iran. He made it clear that any suggestion to drop them was not a reasonable request," the source said.
"He said if Israel could question Syria's relations with Iran then Syria could question Israel's ties with other countries, particularly the United States," the source added, referring to Israel's main ally.
The parliamentarians, including former home secretary and Labor Party member Charles Clarke, are on a trip to Syria to hear first hand the country's take on the Middle East.
Syria and Israel said last week they were having indirect talks mediated by Turkey, the first confirmation since 2000, when talks collapsed over a proposed Israeli withdrawal from the Golan, a fertile plateau occupied by Israel four decades ago.
A week after the announcement, Syrian defense minister Hassan Turkmani visited Tehran to discuss closer military cooperation, Syrian government newspapers said.
Hamas leader Khaled Meshal, who lives in exile in Syria, also made a separate trip to the Iranian capital.
The alliance between Syria and Iran dates to 1980, when Damascus, alone in the Arab world, sided with Iran during the Iran-Iraq war.
Syria reinforced its links with the Islamic Republic over the last few years to counter pressure from the United States, including sanctions imposed by Washington in 2004.
Syria's link with Hezbollah contributed to an expansion of U.S. sanctions on Syria and increased isolation from the West, but European officials praised Syria for its role in this month's agreement that ended the political crisis in Lebanon.
Turkey said the indirect peace talks it is mediating could be upgraded to face-to-face encounters if progress was made.
Syrian forces pulled out in Lebanon in 2005 after a 29 year presence under international pressure following the assassination of former Lebanese premier Rafik al-Hariri, but Damascus retains influence, largely through Hezbollah.
Hezbollah and the Lebanese government say Israel occupies the Lebanese Sheba Farms. The United Nations says Sheba Farms are Syrian land occupied by Israel, not Lebanese.
Want to enjoy 'Zen' reading - with no ads and just the article? Subscribe todaySubscribe now