"We call for an immediate national dialogue. We are ready to make all efforts to have a successful dialogue," he said.
Abbas made his appeal for talks in a televised speech on Wednesday, after months of insisting that Hamas relinquish control of Gaza before dialogue could begin.
Hamas seized control of Gaza in June last year, leaving Fatah's administration in control only of the West Bank.
Taher Nunu, a Hamas spokesman in Gaza, said on Wednesday that the call for dialogue was a "positive step".
"We welcome this call by President Abbas to launch a national dialogue," he said.
Abbas said that if the talks succeeded he would "call for new legislative and presidential elections".
A Yemeni-brokered deal in March were the first direct talks between Hamas and Fatah since Hamas took control of the Gaza Strip.
The deal, signed by both sides, aimed to end the standoff between both sides by returning to the status quo that existed before Hamas seized power.
Also on Thursday, Hamas seized control of the Palestinian water agency in Gaza, according to reports from the Reuters news agency.
The agency is part of an economic stimulus plan for the Palestinian territories spearheaded by Tony Blair, the former British prime minister and now envoy for the Middle East Quartet - made up of the US, UN, Russia and the EU.
The move could put in doubt the future of a desperately needed sewerage project in Gaza.