Hamas's leadership held talks with Mohammed Dahlan - the exiled former Fatah leader in Gaza whose supporters Hamas defeated when it wrested control of the territory in the 2007 civil war - amid hopes he could persuade Egypt to come to the aid of Gazans struggling under the decade-long Israeli-led blockade.
In a overture to its rival Fatah, Hamas agreed to dissolve its governing body in the Gaza Strip, also known as the administrative committee, allow the West Bank-based Palestinian Authority government to operate in its place and hold general elections.
A Palestinian unity government was previously formed in 2014 between Hamas and Fatah, but ended in 2015 after making little progress to reconcile the deep split between the two Palestinian factions.
'We accepted that as a sign of our good will toward reconciliation, ' Hamas official Hussam Badran said.
The last election held by the administrative committee in Gaza was in 2006, when Hamas achieved a surprising victory leading to the political rift between Ramallah and the Gaza Strip.
In July this year it emerged Gaza's Hamas movement was seeking a rapprochement with the Palestinian leader once regarded as its greatest enemy, as the Islamist group faces unprecedented challenges from all sides.
"Hamas invites the consensus government to come to Gaza to practice its mission and carry out its duties in the Gaza Strip immediately, and it accepts holding general elections", Hamas said in the statement.
Hamas has demonstrated a willingness to reach agreement with the Palestinian Fatah movement under the mediation of Egypt.
The coastal enclave of some two million people also has one of the world's highest unemployment rates.
Hamas has been greatly weakened by three losing armed conflicts with Israel since 2008, worldwide isolation and one of the world's highest unemployment rates.
In 2007 a conflict between Fatah, then dominating party in Palestine, and Hamas led to the split of the Palestinian Authority and Hamas taking over the Gaza Strip.
Abbas, now in NY for the annual meeting of the UN General Assembly, has yet to comment on Hamas's announcement.
Azzam Al-Ahmad, who headed Fatah's delegation to the talks in Cairo, told WAFA: "This step will enhance the unity of the Palestinians and end ugly division".
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.