As compensation, Hamas and other Palestinian factions would become part of an advisory committee that would be given a say in the government's decisions.
But Hamas, which won a sweeping victory in the 2006 Palestinian parliament elections, appears unlikely to embrace the Egyptian proposal, which would keep them out of the government.
Delegates at the talks also held meetings with Omar Suleiman, Egypt's intelligence chief.
Suleiman reportedly asked for a final response to the Egyptian compromise proposal when talks resume on May 16.
"Now all the concentration is on the Egyptian proposal, which says that ... any government formed by President Abbas will conduct the contacts with the international community," Nabil Shaath, Fatah's negotiator, said.
Poor relations between Fatah and Hamas further degenerated after security forces loyal to Hamas pushed Fatah fighters out of the Gaza Strip in June 2007.