Taher Nunu, a Hamas spokesman in Gaza, said that the call for dialogue was a "positive step".
"We welcome this call by the president Abbas to launch a national dialogue," he said.
Abbas said that if the talks succeed, "I will 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' siezure of power.