"Israel will study the developments on the ground and will act accordingly", the official said on condition of anonymity.
"All the measures taken recently will end very shortly", Zakaria al-Agha, a senior Fatah leader in the Gaza Strip, told AFP.
The two sides had been meeting in the Egyptian capital this week with the aim of ending a crippling decadeold split between the two sides.
"The legitimate government, the government of consensus, will return according to its responsibilities and according to the law", Fatah delegation chief Azzam Al-Ahmed said at the signing ceremony in Cairo.
A split between Palestine's two major forces, Fatah and Hamas, occurred after the parliamentary elections in Palestine in 2006 when Hamas won.
He said the unity government would "run all institutions without exception", including all border crossings with Israel and in Rafah, Gaza's only access point with Egypt.
It has fought three wars with Israel since 2008 and the blockaded Gaza Strip has faced deteriorating humanitarian conditions.
"It is hard to imagine Hamas giving up its weapons for the sake of reconciliation", Tariq Dana, policy adviser at Al-Shabaka: The Palestinian Policy Network, told Al Jazeera earlier this month. "Unity and national reconciliation among the Palestinian people are our strategic option for moving forward".
Previous attempts at reconciliation have repeatedly failed, and many analysts are treating the latest bid with caution, waiting to see if actual change will occur on the ground.
Struggling with the fallout from the border blockade, Hamas has found it increasingly hard to govern or provide basic services, such as electricity, to Gaza's people.
The publicly-released parts of the agreement did not specify what would happen to Hamas' armed wing. It also added that the Presidential Guard of President Mahmoud Abbas will operate the border, under a reconciliation deal.