As President Donald J. Trump and Prime Minister Benjamin Netanyahu of Israel prepare to meet at the White House on Monday, several new proposals to end the fighting in Gaza and govern the territory are under discussion.

This year’s U.N. General Assembly was dominated by debate about the conflict and the future of the embattled territory. At the end of the sessions last week, President Trump sounded optimistic on reaching a deal to end the war.

But he has made similar pronouncements before, and any effort to stop the fighting still faces significant obstacles. Israel and the Palestinian group Hamas remain at odds over a number of central points, and fighting has intensified in recent weeks with an Israeli ground offensive to take over Gaza City.

Speaking at the United Nations on Friday, Mr. Netanyahu sounded determined to press ahead with the Gaza City campaign. Hamas said on Sunday that it had not received any new proposals from the mediators and that negotiations are at a standstill.

These are some of the latest plans to end the war, set up a new system of postwar governance and address the devastating humanitarian crisis in Gaza.

The Trump plan

Steve Witkoff, the U.S. envoy for peace missions, laid out the broad outlines of an American peace plan in a meeting with leaders of Arab and Muslim-majority countries at the U.N. last week.

Under the plan, Hamas would agree to return all living hostages and remains of former captives within 48 hours of the agreement, according to an Arab official and another person familiar with the matter who spoke on condition of anonymity to discuss sensitive issues. Hamas members who commit to peaceful coexistence with Israel will be granted amnesty under the proposal, and those who want to leave will be guaranteed safe passage out of Gaza, the person familiar with the matter said. The Times of Israel reported earlier on the elements of the proposal.

The American proposal also includes a commitment from both sides to begin a new dialogue on peaceful coexistence, and a pledge that Israel will launch no further attacks on Qatar, according to a senior White House official.

Qatar, an important U.S. ally, has played a central role as mediator in negotiations to end the Gaza war alongside Egypt. Israel launched airstrikes on the Qatari capital, Doha, on Sept. 9 in a failed effort to assassinate a group of Hamas officials — a strike that angered U.S. officials.

But whether Mr. Trump can bring the war to an end will probably depend on how much he is willing to push Mr. Netanyahu, who has adamantly refused to back off his military campaign until Israel achieves its goals. He has also grown more defiant as multiple Western countries last week recognized a Palestinian state.

In an interview with Fox News on Sunday, Mr. Netanyahu said Israel and the United States were still drawing up the plan, and that he did not want to discuss the details yet to avoid pre-empting those conversations.

“We’re working on it; it’s not been finalized yet,” he said. “I hope we can make it a go.”

The Blair plan

One proposal calls for Gaza to be governed by an entity it calls the Gaza International Transitional Authority. Tony Blair, the former British prime minister, may be considered for a role overseeing Gaza after the fighting ends, according to three people familiar with the matter.

The Transitional Authority would be backed by a multinational security force, which would provide security at border crossings and “prevent the resurgence of armed groups, disrupt weapons smuggling and neutralize asymmetric threats,” according to a version of the proposal viewed by The Times.

The Blair proposal also addresses Palestinian fears of permanent displacement from Gaza. It says the Transitional Authority would be empowered to issue “protected departure certificates” so that people who wish to leave Gaza will be guaranteed the right to return to their homes in the future.

The version of the proposal viewed by The Times did not mention Hamas, which led the Oct. 7, 2023, attack on Israel that ignited the Gaza war. But it did say the Palestinian Authority, a rival government to Hamas that administers parts of the West Bank, would have a limited role in governing Gaza. The Authority is more moderate than Hamas and cooperates with Israel on security.

Israeli officials have long criticized the Palestinian Authority, accusing it of corruption, mismanagement and fomenting hostility toward Israel. This proposal calls for significant reforms to the Authority, including its security practices.

It adds that the proposed Transitional Authority and the Palestinian Authority should make decisions “consistent with the eventual unifying of all the Palestinian territory under the” Palestinian Authority.

The French-Saudi plan

A third proposal, which gained the support of 142 countries at the General Assembly, is a plan known as the New York declaration, an effort led by France and Saudi Arabia.

It calls for Israel to withdraw from the Gaza Strip and an international security force organized by the U.N. to step in. Hamas would be banned from governing Gaza and would agree to hand over its weapons to the Palestinian Authority.

The proposal calls for postwar Gaza to be governed by a transitional committee made up of technocrats that would operate under the umbrella of the Palestinian Authority. The authority would agree to hold elections within a year of the cease-fire.

Maggie Haberman contributed reporting.