Deadly clashes between Fatah and Hamas erupted in Gaza in June 2007, after which Hamas set up a rival government, leaving Fatah and the Palestinian Authority running parts of the West Bank not under Israeli control.
The group said in an emailed press statement that it would dissolve a disputed administrative committee in Gaza and wants Abbas' government to come to the coastal enclave.
Since then, the Palestinian leadership has been divided between two rival governments.
President Mahmoud Abbas' Fatah movement on Sunday welcomed a pledge by Hamas to accept key conditions for ending a decade-old Palestinian political and territorial split, MENA news agency reported on Sunday.
Repeated attempts at reconciliation have failed.
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In a statement, it said it would dissolve the committee that rules Gaza and seek elections.
Egypt has been brokering talks with Abbas's Fatah group to implement a deal signed in 2011 in Cairo with Islamist Hamas to end their dispute and form an interim government before elections.
It added that it had decided to make the announcement in response to Egyptian efforts to achieve reconciliation and end internal Palestinian divisions.
Hamas, however, has been greatly weakened by an Israeli and Egyptian blockade, three wars with Israel and global isolation.
Most recently, Abbas had increased pressure on Hamas by asking Israel to reduce power deliveries to the Gaza Strip.
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Punishing measures included reducing electricity payments for the Gaza strip and cutting salaries for civil servants there.
Ahmad and a handful of other Fatah officials were scheduled to travel to Cairo in the coming days to discuss reconciliation with Hamas with Egyptian officials.
Despite Sunday's announcement, any reconciliation deal would still face many obstacles. The deal was not clear whether Hamas is ready to place its security forces under Abbas' control a key sticking point that has scuttled past reconciliation attempts. Gaza's economy is in tatters and residents of the territory have electricity for only a few hours a day.
Since 2007, Israel has maintained a full blockade on Gaza.
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