Hamas invited Palestinian President Mahmoud Abbas to send officials to Gaza to resume control of the coastal enclave the Islamic militant group seized a decade ago.
Hamas has said it will dismantle a contentious committee that has governed Gaza in recent months - answering a key Abbas demand. It has also said it is ready to hand over all government functions to Abbas and to hold elections in Gaza and the West Bank.
"We extend a clear and frank invitation without obstacles for the consensus government to work in Gaza," Haniyeh said after returning from Cairo, where he and other Hamas leaders held rare talks with Egyptian officials.
Hamas is in financial and political distress after years of an Israeli-Egyptian blockade as well as recent economic pressure from Abbas.
The militant group won legislative elections in 2006 and the following year seized control of the Gaza Strip from Abbas' forces, leaving the Palestinian president in charge of autonomous enclaves in the West Bank.
Several past attempts at ending the rift have failed, and thorny issues remain, including security arrangements in Gaza. Hamas has thousands of armed fighters and a sizeable arsenal of rockets and mortar shells. It has always resisted calls to disarm or place its men under Abbas' control.
The two Palestinian factions are also divided over Israel. Abbas has recognized Israel and renounced violence, while Hamas seeks Israel's destruction.
Abbas cautiously welcomed Hamas' intentions on Sunday as he headed to New York for the U.N. General Assembly.
Haniyeh praised the rapprochement between Hamas and Egypt, which cut ties to the militant group and strengthened the Gaza blockade after the military overthrew an elected Islamist president, who had supported Hamas, in 2013.
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