JERUSALEM — President Mahmoud Abbas of the Palestinian Authority and the leader of the rival Islamic group Hamas met Thursday and the sides agreed to go ahead with elections in the Palestinian territories next year, according to officials, even as they failed to resolve differences over an interim unity government to prepare for the vote.

The meeting, in Cairo, was the first between Mr. Abbas, chief of the mainstream Fatah movement, and his rival, Khaled Meshal, the political leader of Hamas, since the two men signed a reconciliation accord in May. Even since then, the leadership of the Palestinian territories has remained divided, with Mr. Abbas’s authority confined to the West Bank while Hamas controls the coastal enclave of Gaza.

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