Hamas had previously demanded that Abbas halt a series of measures taken against the Islamic militant group before sitting down to discuss a reconciliation deal.
Abbas cut electricity in Gaza and slashed the salaries of tens of thousands of public servants in a bid to compel Hamas to dissolve a contentious committee it formed to run the territory in defiance of Abbas' government.
In a statement Monday following a meeting with Egyptian officials in Cairo, the group said it was prepared to dissolve the committee.
The rival Palestinian factions split in 2007 when Hamas violently routed forces loyal to Abbas from Gaza. Repeated attempts at reconciliation have since failed.