A key sticking point in the past was Hamas's refusal to place its security forces in Gaza under the control of the unity government led by Mr Abbas.
Hamas said it had also agreed to hold general elections in order to end the decade-long split.
Fatah, meanwhile, said on Sunday that it welcomed the pledge by its rival Hamas to accept key conditions for reconciliation.
The group said it was "responding to the generous Egyptian efforts, which reflect the Egyptian desire to end the split and achieve reconciliation, and based on our desire to achieve national unity".
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The Muslim Rohingyas have been fleeing from Myanmar (Burma) by the thousands. Aung San Suu Kyi's attends a Myanmar parliament meeting on April 8, 2015.
Hamas has run Gaza since 2007, when it forced troops loyal to Abbas from the coastal enclave a year after defeating his Fatah movement in parliamentary elections.
The takeover led to rival governments, with Hamas in charge of Gaza and President Abbas controlling autonomous pockets of the Israeli-occupied West Bank.
Hamas, who are on the United Nations terrorist list, have controlled the Gaza Strip and the West Bank since 2007.
"The administrative committee is now dissolved, and the government can come to Gaza today to assume its responsibilities and duties", he said.
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Three wins and a draw in four games means that the Red Devils are leading the English Premier League on goal difference. We couldn't be happier". "What I did with him was what I do normally with every player - like Jones".
However, he wondered if "Hamas committee is the only obstacle for reaching full reconciliation and ending internal division", saying that he is "personally consciously optimistic", because there are many questions that need answers.
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.
"If the news is correct, that is good and positive", Fatah Vice Chairman Mahmoud al-Aloul said in a statement posted on Fatah's official Facebook page.
Hamas is also under further pressure from an aggressive policy from Abbas, who governs in the West Bank, and who in June asked Israel to substantially cut its electricity supply to Gaza's 2 million residents.
Chief of the Hamas terror group in Gaza Yahya Sinwar (C-L) visits the border with Egypt, in the southern Gaza Strip city of Rafah, on July 6, 2017.
Chrome to Stop Auto-Playing Videos
That includes ads that have pop-ups, auto-playing video, and "prestitial" count-down ads that delay content being displayed. CNET is a great site, but every damn page of every damn article on the entire damn site autoplays a video when you load it.