Hamas announced the dissolution of the administrative committee created in March 2016 to manage the territory and invited the consensus government led by Prime Minister Rami Hamdallah to arrive in the Gaza Strip to carry out the mission, an official statement said.
It asked the West Bank-based government of Palestinian Authority President Mahmoud Abbas to return to Gaza, which Hamas has controlled since it violently wrested control of the territory more than 10 years ago.
Egypt relayed Fatah demands to Hamas that as a first step, it must dissolve the administrative committee, its de facto government in Gaza, and allow the unity government to take charge.
The Palestinian militant group Hamas says it is aiming for talks with rivals Fatah as it aims to end their decade-long feud. There was no immediate comment from Abbas's government, and a senior Palestinian official was guarded in his optimism.
The two sides have made several attempts at reconciliation.
"Hamas is ready to resume the dialogue with the Fatah movement to implement the Cairo reconciliation agreement of 2011 on the formation of a unity government with other Palestinian factions", the statement said.
The move also comes after a series of Palestinian Authority measures created to pressure Hamas, including reduction of electricity in Gaza and cutting of salaries.
It added that it had decided to make the announcement in response to Egyptian efforts to achieve reconciliation and end internal Palestinian divisions.
Punishing measures included reducing electricity payments for the Gaza strip and cutting salaries for civil servants there.
Despite Sunday's announcement, any reconciliation deal would still face many obstacles. 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.
Israel's increasing restrictions on exit permits for Gaza residents, an escalating sewage crisis that is contaminating the strip's beaches, and high levels of unemployment, are all contributing to a mounting sense of exhaustion in the strip.