Alkhatib said on Sunday that he was willing to hold talks with President Bashar al-Assad's representatives in rebel-held areas of northern Syria to try to end a conflict that has killed about 60,000 people.
The aim of the talks would be to find a way for Assad to leave power with the "minimum of bloodshed and destruction", Alkhatib said in a statement published on his Facebook page.
Sources in the coalition, an umbrella group of opposition political forces, said that Alkhatib, a moderate cleric from Damascus, met international Syria envoy Lakhdar Brahimi in Cairo on Sunday.
Brahimi played a main role in organizing meetings between Alkhatib and the foreign ministers of Russia and Iran, Assad's main supporters, in Munich last week.
The sources said that in their talks on Sunday the two men addressed the question of whether the coalition would formally endorse Alkhatib's peace initiative.
The Syrian authorities have not responded directly to Alkhatib's initiative -- formulated in broad terms last month. But Information Minister Amran al-Zubi on Friday repeated the government's line that the opposition was welcome to come to Damascus to discuss Syria's future in line with Assad's proposals for a national dialogue.
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.
Meanwhile, a Syrian military source yesterday dismissed as unfounded media reports that the armed rebels in Northern Province Aleppo had overrun two bases near the military airport of Ming.
The source, whose remarks were carried by the state-run SANA news agency, said "such false allegations come as part of the desperate attempts to lift the collapsing morale of the armed groups that are facing strikes by our valiant army."
In a related development, a top U.S. military officer said on Sunday he favored the idea of arming Syrian rebels during discussions within the Obama administration about how to help resolve the country's civil war.
General Martin Dempsey, chairman of the Joint Chiefs of Staff, said he thought arming the rebels might help end the crisis more quickly and avert the collapse of government institutions, which could lead Syria to become a failed state.
"Conceptually I thought if there were a way to resolve the military situation more quickly it would work to the benefit not only of the Syrian people but also us," Dempsey told reporters aboard his plane from Afghanistan, where he attended a change-of-command ceremony for NATO-led forces.
"A failed state is defined by the collapse of its institutions," he said. "And so conceptually we thought about ways to prevent that from happening. Conceptually I was in agreement. Now there were enormous complexities involved that we still haven't resolved."
Dempsey and Defense Secretary Leon Panetta acknowledged their support for arming Syrian rebels during a Senate hearing last week, the first time they had been queried about the issue.
The CIA and State Department had recommended arming the rebels last year, but President Barack Obama ultimately decided against pursuing the option.