Sounding conciliatory after raising the political ante against Abbas following his call for national elections last month, Mashaal said the Islamist group Hamas "stretches its hand" to Abbas' Fatah faction to end divisions between the two sides undermining the Palestinian cause.
"Courage dictates that we, as leaders of the Palestinians, be frank with our people and evaluate what compromise has brought us, decide together to suspend or freeze the political settlement process and pursue our real national options," Mashaal told a rally in the Syrian capital.
He said compromise with Israel, starting with the 1993 Oslo Accords, had failed to stop Israeli settlement expansion and brought Palestinians no closer to establishing an independent state in the land Israel has occupied since the 1967 war.
Abbas suspended talks with Israel during the Israeli invasion of Gaza in December and US efforts to re-start them have since failed. Hamas has opposed the talks and rejected Western demands to recognize Israel, renounce armed struggle and accept existing interim peace deals.
"Any leader who insists on the right of return for the Palestinian refugees and on restoring the land, even to the 1967 borders ... must know that the way to do this is not through negotiations or betting on the Americans but through holy struggle, resistance and national unity," Mashaal said.
"Our hand is stretched out to reconcile with our brothers in Fatah and the Palestinian presidency to achieve our national project," he said, but did not make any new proposals for reconciliation after Hamas rejected an Egypt-mediated deal.
Hamas won a Palestinian parliamentary election in 2006, defeating the once-dominant, more secular Fatah, and won a brief civil war the following year in the Gaza Strip against Fatah.
Abbas then sacked the Hamas government and appointed his own administration in the West Bank.