Although the reconciliation talks are viewed as a positive step towards Palestinian unity, they have already experienced their first sign of trouble.
After a decade of division, are there reasons to believe the rival Palestinian factions might finally come together?
Hamas has ruled the territory since 2007, when it seized it from the PA in a near civil war and multiple previous reconciliation attempts have failed.
Following reconciliation efforts between the Palestinian Authority and Hamas, Israeli Defense Minister Avigdor Lieberman criticized the attempt as cynical. The squabbling palestinian are considered as one of the obstacles to a settlement of the israeli-palestinian conflict and one of the causes of the despair of the two million Gazans crammed on their land jammed between Israel, Egypt and the Mediterranean.
Netanyahu's foreign minister at the time, Avigdor Liberman, concurred, saying that Abbas had to decide whether he wanted to make peace with Israel or with Hamas.
U.S. President Donald Trump's envoy to the Middle East, Jason Greenblatt, said in a statement that while Washington welcomed the effort to put the PA back in control of Gaza, any resulting unity government "must unambiguously and explicitly commit to nonviolence, recognition of the State of Israel, acceptance of previous agreements and obligations between the parties, and peaceful negotiations".
The Hamas leader added: "We want a government to dominate the West Bank and the Gaza Strip and carry out its work without any interference from anyone. It is a completely different dynamic on the ground", she told AFP.
"The whole world is watching the efforts at achieving reconciliation between the leaders of the Palestinian people", El-Sissi said in a recorded speech played during a meeting between his intelligence chief, Khaled Fawzi, and Hamdallah.
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If this week's visit was about symbolism, next week the details begin.
At the beginning of the meeting, which took place at the official Gaza residence of Abbas in Gaza, Hamdallah pledged to end the rift.
A key stumbling block is control of security in Gaza.
Hamas's military wing, the Izz ad-Din al-Qassam Brigades, has an estimated 27,000 men under arms.
Hamas could not "copy or clone Hezbollah's experience in Lebanon", he warned on Monday, referring to a situation where an independent armed group exerts major influence on national politics.
Afterwards government spokesman Yusuf Al Mahmud said a full reconciliation deal would take time. "But when Hamas joins the institutions of the Palestine Liberation Organization, which is the umbrella group for all the Palestinian factions, Hamas will be required to accept the principles of the organization and its decisions", Abbas said in an interview on Tuesday, according to the Jerusalem Post.
These conditions are tantamount to the movement dissolving, analysts say.
Pressuring Hamas to loosen its grip on Gaza, he halted payments for Israeli-supplied electricity to the enclave in June, a step that has led to lengthy, daily blackouts.