In a statement, 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".
The Palestinian movement Hamas on Sunday announced to dissolve the Gaza administrative committee and allow the consensus government of President Mahmoud Abbas to govern in its place and hold general elections.
Hamas has run Gaza since 2007, when it forced troops loyal to Abbas from the coastal enclave a year after defeating his Fatah movement in parliamentary elections. Repeated attempts at reconciliation have failed.
Hamas said in its statement it agreed to dissolve the administration running Gaza, allow the reconciliation government to carry out its duties in the territory, to hold elections and enter into talks with Fatah.
Egypt recently invited top Hamas officials to Cairo for reconciliation discussions, and last week, Abbas sent a delegation of representatives to Egypt as well.
Since 2007, Israel and Egypt have maintained a land and sea blockade on the Gaza Strip to prevent attacks.
Hoping to pressure Hamas into relinquishing control of Gaza, Mr Abbas cut payments to Israel for the electricity it supplies to Gaza.More news: How to watch Canelo Alvarez vs. Gennady Golovkin: Stream, time, latest odds
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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.
Egypt has been brokering talks with Fatah to implement a deal signed in 2011 in Cairo with Hamas to end their dispute and form an interim government before elections. "Hamas has now made a courageous, serious and patriotic decision to dissolve the administrative committee (in Gaza)", Barhoum said.
The unemployment rate now stands at 42 percent in Gaza, infrastructure for water and electricity do not meet its residents' basic needs and half of the population relies on humanitarian aid.
Hamas has been weakened by an Israeli and Egyptian blockade, three wars with Israel and global isolation.
However, in a statement made on Monday following a meeting with Egyptian officials in Cairo, the group said it was prepared to start talks with Fatah.
Despite Sunday's announcement, however, any reconciliation deal faces many obstacles.
United Nations officials have called for the blockade to be lifted, but Israel says it is necessary to stop Hamas from obtaining weapons or materials that could be used to make them.