According to the statement, Hamas is also ready to hold general elections.
Hamas has agreed to dissolve the administration that runs Gaza, it said on Sunday, a major step towards handing control of the enclave to a Palestinian unity government after a decade of bitter rivalry with President Mahmoud Abbas.
Hamas and Fatah agreed in 2014 to form a national reconciliation government, but despite that agreement, Hamas's shadow government has continued to rule the Gaza Strip. Repeated attempts have been made by regional forces to achieve a reconciliation between the two parties, but all efforts have so far failed.
Palestinian militant group Hamas said on Sunday that it is ready to dissolve the committee ruling Gaza, and hold a general election for the first time since 2006.
Hamas wants Palestinian President Mahmoud Abbas to lift punitive measures against Hamas in Gaza over the past four to five months, including budget cuts to Gaza for electricity, medical services, salaries. He did not meet with any Hamas leaders however.
Among the demands are fresh elections in the West Bank and Gaza, which Hamas has boycotted due to it winning the last election that led to the split.
Fatah welcomed the statement, and said a bilateral meeting with Hamas would be organised soon.
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Fawzi Barhoum, Hamas spokesman in Gaza said in an emailed press statement that Hamas has positively responded to the big Egyptian efforts, which were exerted to achieve reconciliation and ending more than 10 years of internal Palestinian division.
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.
Abbas Zaki, another senior-level Fatah official close to Abbas, also commended the initiative.
Gaza has been under an Israeli blockade since Hamas violently seized control of the territory from the Palestinian Authority.
Dahlan is sponsored by Egypt and the United Arab Emirates, which both aided his recent re-entry into Palestinian politics through a deal that eased Gaza's chronic electricity crisis and calls for the opening of Egypt's border with Gaza on a permanent basis.