Antony J. Blinken, the U.S. secretary of state, and a Saudi ambassador asserted on Tuesday the possibility of diplomatic recognition of Israel by Saudi Arabia if the Israeli government alleviates the suffering of residents of Gaza and puts Palestinians on a path toward statehood.

During meetings in Tel Aviv, Mr. Blinken said Israel had “real opportunities” to strengthen ties with Arab nations, as he sought to find a political endgame to the Israel-Hamas war in Gaza and calm regional violence arising from the conflict, even as Israel says it is slowing down major combat operations in Gaza.

Mr. Blinken’s comments were a reference to his assertion on Monday night, after talks at a Saudi royal camp in the desert, that Saudi Arabia and other countries remained interested in eventually building normal diplomatic relations with Israel despite the destruction in Gaza. But Arab leaders insist Israel must end the Gaza war first and work toward a Palestinian state, Mr. Blinken said — a position at odds with the Israeli government.

A senior Saudi official made similar points on Tuesday, in the strongest signal since the Oct. 7 Hamas attacks and the start of the war that Riyadh remains open to talks of normalization, as long as Israel takes concrete steps that would benefit Palestinians.

In an interview with the BBC, Prince Khalid bin Bandar bin Sultan, Saudi Arabia’s ambassador to Britain, said that the kingdom’s talks with the United States about normalization had revolved around an endpoint that “included nothing less than an independent state of Palestine.”

“While we still — going forward even after Oct. 7 — believe in normalization, it does not come at the cost of the Palestinian people,” Prince Khalid said.

On Tuesday night, after meetings with a range of Israeli officials, including Prime Minister Benjamin Netanyahu of Israel and the Israeli war cabinet, Mr. Blinken said at a news conference that Israel’s integration into the region was not a substitute for a “political horizon for Palestinians and ultimately a Palestinian state.”

“On the contrary, that piece has to be a part of any integration efforts, any normalization efforts,” he added. “That was also very clear in my conversations during the course of this trip, including in Saudi Arabia.”

What Mr. Blinken left unspoken was the utter reversal that would be required by the Israeli government, which is now controlled by a right-wing coalition. It has opposed Palestinian statehood and also made it an ever-dimmer prospect by expanding settlements in the occupied West Bank, undermining the Palestinian Authority there and taking steps that have helped Hamas retain control of Gaza.

In his talks with Mr. Netanyahu, Mr. Blinken told reporters, the two governments agreed to a plan to have a U.N. team assess northern Gaza to see what conditions were needed for Palestinians to return to their homes there. “This is not going to happen overnight, he said. “There are serious security, infrastructure and humanitarian challenges.”

But Mr. Blinken said he insisted to Mr. Netanyahu that Palestinians returned home as soon as conditions allowed, and also that the United States opposed any efforts to resettle Palestinians outside of Gaza, as some far-right Israeli cabinet officials have proposed. Mr. Blinken said Mr. Netanyahu told him that mass emigration was not the Israeli government’s policy.

Forging normal diplomatic ties between Israel and Saudi Arabia, a leading Arab power and Muslim nation, would be an important political victory for both Israel and the United States.

Before Oct. 7, the main discussions about a long-shot normalization deal had taken place between Riyadh and Washington, with the Saudis asking for important security commitments from Washington. But Mr. Blinken’s statements reveal the terms have shifted, marking the first time since talks began in earnest last year that a top American official has explicitly linked Palestinian statehood to normalization between Saudi Arabia and Israel.

The prospects for the kind of three-way agreement among those two countries and the United States, floated by the Biden administration early last year, have dimmed because of the war: Citizens of Saudi Arabia and other parts of the Arab world are incensed at Israel, given the destruction of most of Gaza and the killings of around 23,000 people, according to the Gaza Health Ministry.

And many Israelis are reluctant to give the Palestinians greater rights or concede to a Palestinian state, with its own military and arsenal, given the horrors of Oct. 7, when Hamas fighters killed about 1,200 people in southern Israel, most of them civilians, according to Israeli officials.

But Mr. Blinken pressed forward on Tuesday, dangling the potential for normalized ties in an apparent effort to try to get Israel to curtail military operations in Gaza and consider a wide-reaching political solution.

“I look forward to sharing with you some of what I’ve heard from countries around the region,” he said in public remarks to Israel Katz, the foreign minister, before the start of their meeting on Tuesday morning. “I know your own efforts, over many years, to build much better connectivity and integration in the Middle East, and I think there actually are real opportunities there.”

“But we have to get through this very challenging moment and ensure that Oct. 7 can never happen again and work to build a much different, and much better, future,” he added.

Arab leaders are moving forward with their own diplomacy on the war. Mahmoud Abbas, president of the Palestinian Authority, plans to travel to Jordan for a summit on Wednesday with President Abdel Fattah el-Sisi of Egypt and King Abdullah II of Jordan to discuss the situation in Gaza, Jordan’s state news agency reported. Mr. Blinken also plans to meet with Mr. Abbas on his trip.

Before flying to Israel on Monday night, Mr. Blinken told reporters in the desert oasis town of Al Ula, Saudi Arabia, that the Saudi ruler, Crown Prince Mohammed bin Salman, had told him in a meeting there that the Saudis still had “a clear interest” in trying to normalize diplomatic relations with Israel.

But there were at least two conditions for that, Mr. Blinken said: an end to Israel’s military offensive in Gaza, and Israel’s agreeing to take practical steps toward establishing a Palestinian state.

Before the Oct. 7 attacks, the Biden administration had been trying to arrange an agreement among the United States, Saudi Arabia and Israel. It would lead to Saudi Arabia establishing normal relations with Israel in exchange for a U.S.-Saudi mutual defense treaty, U.S. cooperation on a Saudi civil nuclear program and approval of more arms sales from the United States. The New York Times reported last month that President Biden was ready to relax restrictions on sales of offensive weapons to Saudi Arabia.

In those earlier talks, Prince Mohammed was not insistent on a Palestinian state or a concrete pathway to establish one, U.S. officials said. Saudi officials assert that the Palestinian issue has been essential to the country’s leaders.

In September, Prince Mohammed said that the talks between Saudi and American officials were getting “closer every day” to a deal in which Saudi Arabia would formally recognize Israel. In an interview with Fox News, he did not specifically call for a Palestinian state, saying only that he wanted to see “a good life for the Palestinians.”

However, Prince Khalid’s and Mr. Blinken’s comments described Palestinian statehood as an explicit condition.

In its decades-long official policy, Saudi Arabia has conditioned the establishment of ties with Israel on the creation of a Palestinian state. Saudi officials made that a central pillar of the 2002 Arab Peace Initiative led by the kingdom.

It is unclear how Saudi officials see a pathway to normalization unfolding now, particularly since they face deeply negative public opinion toward Israel. A recent poll found that 96 percent of Saudis believe that Arab countries should cut all ties with Israel to protest the war in Gaza. Only 16 percent of the Saudis surveyed said that Hamas should stop calling for the destruction of Israel in order to accept the creation of Palestinian and Israeli states side by side.

While Saudi Arabia has grown more autocratic over the past eight years, analysts say that Prince Mohammed, the country’s de facto leader, must still take public opinion into account as he weighs decisions.

In addition to meeting with Mr. Abbas soon, Mr. Blinken plans to travel to Egypt. He has visited Turkey, Greece, Jordan, Qatar, the United Arab Emirates and Saudi Arabia since beginning his latest diplomatic mission on Friday.

Another focal point of his discussions has been preventing the war in Gaza from widening, given the recent escalation of violence involving Hezbollah in Lebanon, Houthi fighters in Yemen and Iran-backed militias in Iraq and Syria.

Mr. Blinken told reporters those talks centered on the exchanges of fire between Israel and Hezbollah in the north. The Biden administration has been talking to Lebanon and sending messages to Hezbollah, and Mr. Blinken said Israeli officials still believe a “diplomatic path” is the best way to achieve security in the north.