Al-Ahmad also praised Egypt's role in helping achieve Palestinian national reconciliation and providing a venue for Hamas-Fatah talks.
The Western-backed mainstream Fatah party lost control of Gaza to Hamas in fighting in 2007. Leaders of both Palestinian factions began met in Cairo for an extended dialogue in order to initiate a mechanism for implementing the reconciliation agreements reached in the last few years.
According to a Palestinian source close to the Cairo talks, the agreement calls for the Fatah-led Palestinian unity government to assume full political and administrative control of the Gaza Strip by Dec.1.
The crossing with Egypt may require more time for the handover, with construction work now underway there. Specifically, Fatah will reportedly have joint control over a key Gaza border crossing, and will in return lift some punitive sanctions.
Fatah, the more moderate of the two groups, previously controlled Gaza but was ousted by Hamas a decade ago, leaving Palestine split in two.
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.
The agreement, which is a reactivation of a previous deal signed in 2011, was signed in the presence of Egyptian Intelligence Minister Khalid Fawzi.
Cairo is now leading efforts to heal a decade-long political split between Gaza-based Hamas and the West Bank-based Fatah movement of Palestinian President Mahmoud Abbas.
Islamist movement Hamas is blacklisted as a terrorist organisation by the United States and the European Union. Hamas and Israel fought three devastating wars over the past decade.
"We are meeting in Cairo in hopes of formulating a roadmap titled National Reconciliation", wrote Hamas member Izzat Reshiq on his Twitter account earlier this week.
Egypt has also agreed to provide fuel to the Gaza Strip for electricity generation.
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. Israel and Egypt imposed a blockade on the territory, severely restricting Palestinians from leaving the territory and goods from entering.
The new deal is understood to cover border crossing arrangements, Hamas' arsenal and the livelihoods of thousands of public servants.
Reconciliation could also pose a dilemma for global efforts to reach an Israeli-Palestinian peace deal since Hamas has not recognised Israel, unlike the Abbas-led Palestine Liberation Organisation.