In a statement issued overnight, Hamas said it was "responding to the generous Egyptian efforts, which reflect the Egyptian desire to end the split and achieve reconciliation, and based on our desire to achieve national unity".
Hamas said in a statement on Sunday that it has dissolved its shadow government, that it will allow the reconciliation government to operate in Gaza and that it agrees to hold elections and enter talks with Fatah.
Attempts by the groups to form a unity government in Gaza and the West Bank since then have failed.
Hamas, however, has been greatly weakened by an Israeli and Egyptian blockade, three wars with Israel and worldwide isolation.
Some polls show that if parliamentary elections were held now, Hamas would win them in both Gaza and the Israeli-occupied West Bank, the seat of Abbas's Palestinian Authority. The UN has even ruled that enclave, one of most densely populated areas in world (2 million inhabitants) would become "unlivable" by 2020.
In March, Abbas stepped up pressure on Hamas after it formed the contentious committee that runs Gaza.
On Friday, Abbas brought an official Fatah delegation to Cairo to join the reconciliation dialogue that Egypt has been sponsoring, before which Abbas chaired a meeting for Palestine Liberation organization executive committee in Ramallah.
For the past several months, Fatah and its chairman Mahmoud Abbas have called on Hamas to make and implement such an announcement.
However, he wondered if "Hamas committee is the only obstacle for reaching full reconciliation and ending internal division", saying that he is "personally consciously optimistic", because there are many questions that need answers. But Associated Press reported that it is not yet clear whether Hamas is ready to place its security forces under Abbas's control - a major sticking point in the past.
The electricity crisis, aimed at forcing Hamas to return the territory to the Palestinian Authority's control, comes on top of Gaza's many other woes.
Representatives for Abbas, who is in NY ahead of the U.N. General Assembly this week, could not be reached for comment, nor could Fatah representatives presently in Egypt, which has been hosting talks with Hamas.
United Nations officials have urged Israel to lift its decade-long blockade of Gaza.