The July-August war in the besieged Gaza Strip destroyed or partially damaged tens of thousands of homes, leaving 100,000 Gazans homeless.
"Some 90,000 partially-damaged homes have already been repaired in coordination with the United Nations," Mufid Hasayneh told journalists in Gaza City.
"In the coming days, the operation of reconstructing those totally destroyed will begin," he said.
Some 18,000 homes were destroyed or severely damaged, according to UN figures, and reconstruction of the war-wracked coastal territory has been slow.
Israel's ongoing blockade of Gaza, now in its ninth year, has been blamed, as well as the lack of international donor support to the territory, which is ruled by the Islamist movement Hamas.
Hasayneh said that Israel had allowed only 128,000 tonnes of cement into the Strip since the war ended.
Israel says more than 1.1 million tonnes of construction material have been allowed in since October 2014 through the Kerem Shalom goods crossing, which it controls.
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"We (the Palestinians, the UN and Israel) have come to an agreement about the mechanism to allow construction materials to enter from the Israeli side," Hasayneh said.
The mechanism, he said, would stipulate that owners of destroyed houses be vetted in order to receive building materials.
Homeowners would register with local authorities to obtain a building permit, after which their details would be passed onto the housing ministry, headquartered in Ramallah -- the seat of the Western-backed Palestinian Authority.
The ministry would then work with Israeli authorities to get the final go-ahead for Gazans to rebuild their houses.
Hasayneh did not elaborate on why there was a need for a vetting process.
But Israel limits the amount of building materials allowed into Gaza, fearing that metal and concrete could be used by Palestinian militants to make weapons such as rockets, and to build tunnels.
Critics of the blockade have called for it to be fully lifted to allow reconstruction, warning that an ongoing humanitarian crisis could fuel further conflict.
The war killed 2,200 Palestinians and 73 people on the Israeli side.