Hamas, which controls the Gaza Strip, is expected to take part in Egyptian-sponsored unity talks between Palestinian groups on Wednesday.

Washington supports Cairo's mediation, although it regards Hamas as a terrorist group.

Souring relations

Kerry also said that there are possibilities for "real co-operation" between the two nations.

He said he was encouraged by the "very long, candid, open" discussion with President Bashar al-Assad and that he sees the possibility of progress ahead.

"While we will disagree on some issues for sure, what I heard and what I will take back with me and, hopefully, what we could put in place to take advantage of it, is the possibility of real co-operation on a number of different issues beginning immediately, beginning soon," Kerry said. 

Bouthaina Shaaban, a political adviser to al-Assad, told Al Jazeera that the tone of the meeting was very good.

"The meeting was very candid, very frank and very constructive," she said.

Relations soured under the Bush administration, and Kerry and other members of Congress who have come to the Syrian capital in the last week explored the possibilities for better relations after President Barack Obama signaled he wanted to talk to opponents.

Syrian understanding

Syria's support for Hamas and Hezbollah has drawn the ire of Washington, which has also accused Syria of allowing foreign fighters to cross into Iraq.

Shaaban told al Jazeera that Syria was offering the US its understanding of the region.

"Hamas and Hezbollah are resistance groups because there is an Israeli occupation," she said.

"The meeting was very candid, very frank and very constructive"

Bouthaina Shaaban,  political adviser to al-Assad.

"The starting point is to end the occupation and to allow the Palestinian people to live in dignity and freedom as the US always called for dignity and freedom." 

Syria, which staunchly opposed the 2003 invasion, insists it is doing all it can to safeguard its long, porous border.

Relations soured further when the Bush administration pulled the US ambassador out of Syria in 2005.

The move was in protest against Syria's suspected role in the assassination of Rafiq al-Hariri, the former Lebanese prime minister.

Damascus denied involvement in his death, but in the uproar that followed, it was forced to withdraw its troops from Lebanon, ending a 29-year military presence.