Alkhatib has headed the Syrian National Coalition since it was founded last December in Qatar with Western and Gulf backing. He has quietly built a student following and links with civic and religious figures across Syria.
His latest offer of talks coincided with opposition reports of fighting moving closer to central Damascus, after a rebel push into the east of the capital last week.
The Local Coordination Committees, a network of grassroots activists, said clashes broke out yesterday in the al-Afif neighbourhood of Damascus, which is adjacent to a presidential complex.
The organization said 77 people were killed in Syria yesterday, including 16 people who it said had been executed by Assad's forces in the eastern city of Deir al-Zor. Such reports are impossible to verify as Syria severely restricts access for independent media.
The war is pitting Mr. Assad's minority Alawite sect, an offshoot of Shi'ite Islam that has dominated Syria since 1960s, against the Sunni majority that has led the protest movement.
When Alkhatib made his offer of talks last month, he made this conditional on the authorities starting to release tens of thousands of political prisoners jailed since the eruption of the 22-month uprising.
The United Nations said on Friday that it saw a glimmer of hope in Alkhatib's offer.
UN Under-Secretary-General for Political Affairs Jeffrey Feltman said the offer was "the most promising thing we've heard on Syria recently".