JERUSALEM — President Mahmoud Abbas of the Palestinian Authority said Thursday night that he had reached an agreement with Israel and the United Nations to allow imports of reconstruction materials into the Gaza Strip, apparently bypassing Hamas to fulfill a key tenet of the cease-fire agreement that halted hostilities on Aug. 26.

A United Nations diplomat confirmed that the deal was due to be finalized and announced on Friday. Mr. Abbas did not provide specifics about when the imports might begin, how much would be allowed or who would control the process. Neither the Israeli prime minister nor the Israeli agency responsible for coordinating activities in Gaza returned telephone calls.

But at an evening meeting of the Palestinian leadership, Mr. Abbas said that a former minister and a United Nations representative had “signed an agreement which allows the entry of all materials to Gaza and the exporting of what’s possible to export from Gaza abroad, which will alleviate the living burdens on the people.” The comments were broadcast on television.