Hamas statement, which consisted of four points, also said that the movement accepted to hold the general, presidential and legislative elections in the Palestinian territories, the West Bank, Gaza and east Jerusalem.
File: Palestinian Authority President Mahmoud Abbas, left, and Prime Minister Ismail Haniyeh from Hamas, right, raise their linked arms as they move through the crowd at a special session of parliament in Gaza City, March 17, 2007.
Repeated reconciliation attempts have failed since the Hamas militants drove forces loyal to Abbas out of the Gaza Strip in 2007, a year after defeating Fatah in parliament elections.
Conditions also include dissolving the contentious Gaza administrative committee - the de facto government in the region - and allowing an Abbas-led 'unity government, ' who could take control within a matter of days.
Hamas also stated it would dismantle its administrative committee that now rules the Gaza Strip.
In Sunday's statement, Hamas spoke of the "dissolution" of what is known as the administrative committee, which was seen as a rival government to Abbas's administration.
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.
The negotiations were "an expression of Egyptian interest in Palestinian reconciliation and ending the division, and our interest to realize the hopes of the Palestinian people by achieving national unity", CNN quoted Hamas as saying. Gaza's economy is in tatters and residents of the territory have electricity for only a few hours a day.
The Hamas capitulation follows months of repression on the part of the Palestinian Authority, which deprived the Gaza Strip f electric power.
Hamas has always been accused by the Egyptian government of aiding the brutal Islamic insurgency in Egypt's restive North Sinai region, but in recent months, Hamas has beefed up security along Gaza's southern border with Egypt, seeking to assure Cairo that it is fighting IS sympathizers.
The official spokesperson reiterated the Government's full commitment to the implementation of the Cairo agreement which was signed by the Palestinian factions.
Fatah official Azzam al-Ahmad said the Abbas group would hold talks with Hamas to work out details of the pact.
"Hamas wants to improve the situation in Gaza, but it doesn't want to give up control of it", Bjorn said.