Secretary of State Antony J. Blinken arrived in Israel on Sunday to try to clinch a deal that could end the war in Gaza, even as the Middle East remained on edge amid the looming threat of wider regional conflict.

The visit, part of an intensive diplomatic campaign led by the Biden administration, comes days after Israel’s negotiating team held talks in Qatar with senior American officials, as well as Qatari and Egyptian representatives who are mediating between Israel and Hamas.

Those talks ended without a major breakthrough, but the White House said on Friday that the United States had put forward a “bridging proposal,” with Egyptian and Qatari support, aimed at closing the remaining gaps between the sides. It said that teams would continue to hash out details and that senior negotiators hoped to reconvene in Cairo before the end of this week to finalize an agreement.

While the Biden administration had suggested that the process was “now in the end game,” Prime Minister Benjamin Netanyahu of Israel cautioned on Sunday that the negotiations were “very complex” and called his approach to the talks one of give and take — “not give and give.”

“There are things we can be flexible about, and there are things we cannot be flexible about,” he said in remarks recorded at the beginning of his weekly cabinet meeting.

“We know very well how to distinguish between the two,” Mr. Netanyahu added, saying that he was insisting on certain principles that he considered vital for Israel’s security.

Mr. Blinken landed in Israel on Sunday evening. On Monday morning, he is scheduled to meet in Jerusalem with Mr. Netanyahu, whom some officials have accused of stalling by adding new conditions for a deal. Mr. Blinken will also meet with Israel’s president, Isaac Herzog, and the defense minister, Yoav Gallant, according to senior State Department officials. On Tuesday, Mr. Blinken will travel to Egypt to continue his efforts to broker an agreement.

Osama Hamdan, a Hamas spokesman based in Beirut, told Al Jazeera English on Sunday that the Israeli side had introduced new ideas in the cease-fire negotiations and was not prepared to withdraw all its forces from Gaza or commit to a permanent cease-fire — conditions that the group has set for any deal. Israel has balked at making such commitments from the outset.

The deal that Mr. Blinken is hoping to help seal would be carried out in three phases and is based on principles laid out by President Biden on May 31, then subsequently endorsed by the United Nations Security Council. It would usher in a cease-fire in Gaza and see hostages held in the enclave freed in exchange for Palestinian prisoners and detainees held in Israel.

The Biden administration has created a degree of linkage between the cease-fire efforts and the threat of Iranian-led retaliation against Israel for the back-to-back assassinations of senior figures from Hezbollah, the Iranian-backed Lebanese militia, and Hamas in Beirut and Tehran in late July.

Mr. Biden said that part of the reason he was sending Mr. Blinken to Israel — beyond continuing “intensive efforts” to conclude a deal — was “to underscore that with the comprehensive cease-fire and hostage release deal now in sight, no one in the region should take actions to undermine this process.”

Mr. Netanyahu warned on Sunday that Israel was prepared to meet any threat, defensively and offensively, saying the country was “determined to exact a very heavy price” from anyone who dared to attack it.

In the meantime, the fighting in Gaza, where local authorities say more than 40,000 Palestinians have been killed since the war began, has continued. The Gaza Civil Defense emergency service said on Sunday that 14 people were killed in strikes in Nuseirat and Deir al-Balah, in central Gaza.

The Israeli military did not immediately respond to a request for comment. In an earlier statement, the military had said that its troops were operating in the areas of Khan Younis and Deir al-Balah, where Israeli aircraft had “struck targets.”

Reporting was contributed by Hiba Yazbek, Gabby Sobelman, Myra Noveck, Johnatan Reiss and Robert Jimison.