"About 1,000 tonnes of cement and building materials will enter the Gaza Strip for storm damage restoration and other projects of UN agencies," the Israeli defence ministry said in a statement.
A fierce winter storm hit the Palestinian enclave in December, with strong winds and heavy flooding causing damage to homes and infrastructure.
The United Nations Relief and Works Agency, which cares for Palestinian refugees, said it had been given the go-ahead for new construction but that the work was unrelated to storm repairs.
UNRWA said delivery was expected during the coming week.
The defence ministry statement said Israeli authorities "spoke with senior officials in the Palestinian Authority" and informed them of the decision.
But Raed Fatuh, the Palestinian Authority official in charge of the entry of goods into Gaza, said "the Palestinian side has not been officially informed about this".
He added that there were "already 10 international projects that are receiving construction materials via Israel twice a week."
In December it said it would allow renewed shipments but only for use in UN projects.
The import of steel and cement for private use has been banned, except for a brief interlude, since the Islamist group Hamas seized power in Gaza in 2007 for fear it would use such materials to build tunnels and fortify its fighters' positions.
The territory has been under an Israeli blockade since 2006, when Gaza militants snatched an Israeli soldier who was released in a prisoner swap deal in 2011.
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