A statement from Netanyahu's office said that Israel "will examine developments in the field and act accordingly".
"Israel and the worldwide community should insist that the Palestinian unity government accept the conditions of the Quartet and Security Council Resolution 1850: recognition of Israel, a commitment to the two-state solution, and the cessation of terror and incitement", a statement from Peretz's office said.
A senior Fatah leader in the Gaza Strip, Zakaria al-Agha, said that Abbas "will be in Gaza within less than a month".
Security cooperation between Fatah and Hamas could include, among other things, the deployment of 3,000 Fatah security officers, who would join the Gaza police force over a period of 12 months.
Meanwhile, Egypt invited the convening of a meeting in Cairo on 21/11/2017 for all the Palestinian factions that signed the Palestinian National Accord Agreement on May 4, 2011.
The accord will see the consensus government officially take full administrative control of Gaza by December 1, according to a statement issued by Egypt's state media center.
Egypt has kept the Rafah border crossing closed for most of the last decade.
Egyptian chief of intelligence, Khalid Fawzi, presided over the signing as Hamas' representative, Saleh al-Arouri, and Fatah's negotiator, Azzam al-Ahmed, signed on.
Egypt has previously attempted to help Hamas and Fatah create a united government for Gaza and the West Bank.
The official was referring to the diplomatic Quartet on Middle East peace, which includes the United Nations, the United States, the European Union and Russian Federation. Internal Palestinian strife has been a major obstacle to peacemaking, with Hamas having fought three wars with Israel since 2008 and continuing to call for its destruction. A small number of people, mainly medical patients, business people and aid workers, use the Erez crossing to enter Israel, usually bound for the West Bank.
Over the past decade, each side deepened control over its territory, making it increasingly hard to forge compromises, and repeated attempts at reconciliation failed.
The latest reconciliation efforts come as US President Donald Trump has sought to revive peace talks between Israel and the Palestinians and met separately with Abbas and Netanyahu on the sidelines of the United Nations General Assembly in NY last month.