Prime Minister Benjamin Netanyahu of Israel was set to meet President Trump in Washington on Monday as each pushed his own priorities on Gaza, Iran and other critical issues in the Middle East.

Mr. Trump wants to secure a cease-fire deal in Gaza to stop the fighting between Israel and Hamas. Mr. Netanyahu and Hamas have both thrown up obstacles. Hamas wants strong guarantees that the talks will lead to a permanent end to the war, and Mr. Netanyahu has vowed to carry on fighting until Hamas is eliminated.

Mr. Netanyahu, after Israeli and U.S. strikes on Iran in June, has to contend with Mr. Trump’s desire to seek a diplomatic deal with Iran over its nuclear program — an issue he has long viewed with suspicion.

Here’s what’s at stake in the upcoming meeting between the two leaders, their third since Mr. Trump returned to office.

The future of the Gaza war

Many in Israel and Gaza hope Mr. Netanyahu’s meeting with Mr. Trump will pave the way for a new truce that would end 21 months of war and free the remaining hostages in exchange for Palestinian prisoners.

Israel and Hamas have previously agreed to two short-lived cease-fires. The last one, which Israel ended in mid-March, saw more than 1,500 Palestinian prisoners released during exchanges for 30 hostages and the bodies of eight others.

Mr. Trump has said that Israel and Hamas could reach a new agreement as soon as this week, but past efforts to broker a comprehensive cease-fire have failed. The latest proposal being discussed stipulates a 60-day truce during which both sides would negotiate an end to the war.

Both Israel and Hamas may now have reasons to agree to a temporary truce. As Mr. Netanyahu’s plane headed west to Washington, Israeli negotiators traveled east to the Gulf emirate of Qatar for indirect talks with Hamas about the details of the accord.

Mr. Netanyahu, buoyed by what Israelis see as a successful attack in Iran, may now have greater flexibility to make tough concessions in Gaza. Hamas does not want to be blamed by Gazans — who have endured nearly two years of deadly attacks and hunger — for snubbing a truce.

More than 57,000 people have been killed in Gaza, according to the Gaza health ministry, which does not distinguish between civilians and combatants. The war began with Hamas’s October 2023 assault on Israel that killed roughly 1,200 people and saw 251 others taken hostage. About 50 hostages remain in Gaza, about 20 of them alive, according to the Israeli authorities.

But securing a permanent end to the war will be much more challenging.

Mr. Netanyahu has vowed not to end the war before Hamas’s elimination. Hamas has refused to release all of the remaining hostages unless Israel withdraws its forces and agrees to effectively leave Hamas in control of Gaza.

Netanyahu’s hopes for regional deal-making

One big question is whether Mr. Trump is able to wield enough carrots and sticks to cinch both the 60-day truce and the permanent cease-fire.

U.S. officials have hoped to sweeten the deal for Mr. Netanyahu by linking the end to the war in Gaza with a potential diplomatic reshuffle in the Middle East that would ultimately see Arab countries formally cement ties with Israel.

Such a diplomatic win for Mr. Netanyahu would help him to sell a cease-fire more easily at home, where his right-wing coalition partners firmly reject any truce that would leave Hamas in power. Mr. Netanyahu has also made normalizing Israel’s relations with its once-hostile neighbors — particularly Saudi Arabia — a key ambition.

But Saudi Arabia, like other Arab states, is unlikely to agree to normalize relations with Israel unless there is an end to the Gaza war. Riyadh has also demanded a stiff price from Washington, including a civilian nuclear program and defense pact, before it agrees to normalize ties.

In addition, Syria and Israel are engaged in “meaningful” talks through the United States that aim to restore calm along their border, Thomas J. Barrack Jr., one of President Trump’s key envoys to the Middle East, said in an interview last week.

Nuclear talks with Iran

Mr. Netanyahu and Mr. Trump will also discuss American efforts to craft a new accord with Iran about the country’s nuclear program in the wake of the joint U.S.-Israeli attacks last month.

“We’re working on a lot of things with Israel, and one of the things is probably a permanent deal with Iran. They have to give up all of the things that you know so well,” Mr. Trump told reporters on Sunday.

While Mr. Trump is considering a new nuclear pact with Iran, Mr. Netanyahu has long viewed any deals with Tehran with enormous suspicion. He was against the previous U.S.-led accord with Iran, from which Mr. Trump withdrew in 2018.

Before Israel started attacking Iran on Jun. 13, the Trump administration had held repeated rounds of negotiations with Iranian officials over the future of their nuclear program. In the subsequent conflict, the U.S. joined in by bombing three Iranian nuclear sites.

There have been mixed assessments of what that attack accomplished. While the Pentagon said Iran was set back by one to two years, others, including the United Nations’ nuclear watchdog, said that Iran could begin enriching uranium again in a matter of months.