Syrian National Coalition leader Moaz al-Khatib's surprise move came after UN envoy Lakhdar Brahimi said the war had reached "unprecedented levels of horror," and UN chief Ban Ki-moon warned of a "catastrophic" situation in Syria.
Khatib said via his Facebook page he is ready for dialogue with officials of the government with some conditions, including that "160,000 detainees" are released and that passports for exiled citizens be renewed in embassies abroad.
Until now, Syria's main opposition groups have said they are only prepared to enter into dialogue on ways to end the 22-month conflict if Assad steps down.
"I announce I am ready for direct discussions with representatives of the Syrian regime in Cairo, Tunis or Istanbul," Khatib said.
"I became aware thanks to the media that the regime in Syria has called on the opposition to enter into dialogue," said Khatib, who heads the main Syrian opposition umbrella group.
Assad proposed earlier this month a national dialogue to end Syria's crisis, and he made it clear this would only apply to groups not linked to the armed insurgency.
Khatib said the unprecedented statement expressed his own opinion only and that his group would meet on Thursday to discuss the proposal.