Antony J. Blinken, the U.S. secretary of state, met on Wednesday with Mahmoud Abbas, the leader of the Palestinian Authority, to discuss Israel’s war against Hamas in Gaza and the role that the authority might play there when the conflict ebbs.

Mr. Blinken traveled in a convoy from Tel Aviv in Israel to Ramallah, the seat of the authority, in the Israeli-occupied West Bank. The two men shook hands outside the authority’s headquarters and sat down for talks with their aides.

The Biden administration has said it envisions a role for the Palestinian Authority in governing both the West Bank and Gaza. Hamas has run Gaza since it won elections in the tiny coastal strip in 2006 and violently drove out Fatah, the group now in charge of the authority in the West Bank.

President Biden has also said Israel must allow for the formation of a Palestinian state, arguing that a political solution is the only way out of the decades-old conflict between Israelis and Palestinians. Mr. Blinken reiterated that view in a news conference in Tel Aviv on Tuesday after meetings with Israeli officials. He also said Saudi Arabia — whose ruler, Crown Prince Mohammed bin Salman, he met with on Monday — was still willing to consider establishing normal diplomatic relations with Israel, but only if Israel agreed to concrete steps toward the establishment of a free and independent Palestine.

Benjamin Netanyahu, the prime minister of Israel, and his right-wing government have rejected the notion of a Palestinian state, and Mr. Netanyahu said years ago that Israeli officials should support a strong Hamas in Gaza in order to undermine the Palestinian Authority and the idea of a unified Palestine. He has also rejected any substantial role for the authority in Gaza.

After meeting with Mr. Abbas, Mr. Blinken planned to fly to Bahrain for more talks on the war. The Bahrain stop was a last-minute addition to his multiday diplomatic mission across the eastern Mediterranean and the Middle East that began last Friday. Mr. Blinken plans to meet in Cairo later in the trip with the president of Egypt, President Abdel Fattah el-Sisi.

Mr. el-Sisi and Mr. Abbas are expected to be in Aqaba, Jordan, later on Wednesday for a crisis leadership summit called by King Abdullah II.

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