President Biden will visit Israel tomorrow after accepting an invitation from Benjamin Netanyahu. Biden will be following his secretary of state, Antony Blinken, who was in Israel yesterday for the second time in the past week, after already having visited Egypt, Qatar, Saudi Arabia and elsewhere.

In today’s newsletter, we’ll explain what the U.S. is hoping to accomplish with this flurry of diplomacy over the past few days.

The U.S. is not trying to prevent an Israeli invasion of Gaza. Any country attacked as Israel was on Oct. 7 — with Hamas’s killing of more than 1,400 people and kidnapping of at least 199 — would be likely to respond militarily. Israel is no longer willing to accept Hamas’s control over Gaza, given that Hamas is a terrorist group, according to the U.S. and E.U., and has refused to recognize Israel’s right to exist.

“Israel is going after a group of people who have engaged in barbarism that is as consequential as the Holocaust,” Biden said in a “60 Minutes” interview. “Israel has to respond.”

A major Israeli response is important partly to send the message that terrorism doesn’t pay, American officials believe. Israel would like to repeat the experience of 2006, when the leader of Hezbollah — the Iranian-backed militia that controls southern Lebanon — said he regretted kidnapping two Israeli soldiers because of Israel’s fierce response. “If I had known,” Hassan Nasrallah, the Hezbollah leader, said later that year, “would I do it? I say no, absolutely not.”

Dennis Ross, a Middle East adviser to U.S. presidents of both parties, told The Times that part of Blinken’s task when talking with Arab governments was “to remind everybody that Hamas can’t be seen as winning. Hamas must be seen as decisively losing.” In this case, losing probably means the capture or death of many top Hamas officials.

A wider Middle Eastern war is among the Biden administration’s biggest fears. It would lead to even worse loss of life and could draw equipment and attention away from Ukraine as well as cause a global economic downturn through higher oil prices.

The most plausible route to a wider war would involve fighting between Hezbollah and Israel, along Israel’s northern border, and maybe even direct fighting between Iran and Israel. Much of recent U.S. diplomacy seems aimed at avoiding this outcome. Blinken has spoken with the Qatari government and others about urging Iran not to get more involved.

The Biden administration has also moved several warships to the eastern Mediterranean Sea. The ships are meant to make Iran and Hezbollah fear that the U.S. could decimate Hezbollah in the event of a wider conflict. “That’s a very significant show of force,” Natan Sachs, a Middle East expert at the Brookings Institution, told us.

For now, U.S. officials believe that Nasrallah, who remains Hezbollah’s leader, does not want an all-out war with Israel. But these maps show where tensions are rising in the region.

Even if Israel destroys Hamas’s leadership, nobody knows what would come next. And some Israeli officials now seem too angry to think about this question. “I used to say: ‘Think then act,’” Jacob Nagel, a top former Netanyahu aide, told The Wall Street Journal. The Hamas attacks “changed all the rules of play,” he added.

If Israel pursued a maximal war with little concern for Palestinian casualties, it could create such anger in the region that other Arab governments would refuse to work with Israel — just as Hamas hopes. Many experts think that one aim of Hamas’s attacks was erasing the recent progress between Saudi Arabia and Israel toward a diplomatic agreement.

“The trick here is that the U.S. has to embrace Israel and acknowledge their need for vengeance, self-defense and deterrence while at the same time prevent them from overreacting in a way that hurts them long-term,” Michael Crowley, a Times correspondent, said.

A tangible example of U.S. lobbying appears to be the delay in Israel’s ground invasion, which will give more Gazans time to flee south, away from important Hamas bunkers and weapons caches. (The Israeli military allowed a Times journalist to view a cellphone-tracking system of the evacuation, hoping to show that it was doing what it could to reduce harm to civilians.)

Longer term, there will be more difficult choices. Many steps that Israel could take to reduce civilian casualties in Gaza, such as advance warnings of attacks, would also weaken its attempts to destroy Hamas’s control. And it remains unclear who will run Gaza if not Hamas.

Still, some analysts can imagine a future that’s better than the past, as The Washington Post’s David Ignatius has noted. This future might involve the Palestinian Authority — which does recognize Israel’s right to exist — running Gaza, with help from Saudi Arabia and other Arab governments, as well as the United Nations.

“It’s not impossible for seemingly intractable conflicts to find solutions,” Emma Ashford wrote in Foreign Policy. “The surge in U.S. support to Israel now gives Washington leverage that it hasn’t had in a long time, and the Arab states would be thrilled to find a way out of this mess.”

“I have no higher priority than the safety of Americans being held hostage around the world,” Biden said last week. Of the roughly 200 hostages that Hamas is holding, a handful or more may be American.

U.S. officials are making diplomatic efforts to win the hostages’ release and would celebrate any successes. But many experts believe that Hamas is unlikely to release many, if any, hostages. In that case, the U.S. will likely advise Israel on rescue missions.

Related: Biden’s trip is a gamble. It is both dangerous and will tie him to the Israeli ground invasion that seems almost certain to follow.

  • The federal judge overseeing Donald Trump’s Jan. 6 trial imposed a partial gag order, barring Trump from attacking witnesses and prosecutors.

  • Representative Jim Jordan won over several Republicans but remained short of the support he needs to become House speaker. Votes are planned for today.

  • Oprah Winfrey pitched Mitt Romney on the idea of running for president as an independent in 2020 with her as a running mate, according to a coming biography.

  • After a lawsuit, thousands of families whom the Trump administration separated at the border were given a path to legal residency.

  • Massachusetts will no longer guarantee emergency housing for new migrant arrivals beginning next month.

After Israel defeats Hamas, it will have to rebuild Gaza. Start by creating an economy and school system the locals can trust, Thomas Warrick, a former U.S. official, writes.

Student organizations that blamed Israel for Hamas’s attacks showed a major problem with U.S. universities, Ezekiel Emanuel writes.

An American puzzle: Census categories for race and ethnicity have shaped how the nation sees itself. Read how they have changed over the last 230 years.

#MentalHealth: What happened when academics collaborated with influencers to inject more mental health content into TikTok feeds?

Ask Well: Dogs can enrich our lives, but they can also make us sick. Here’s how to reduce your risk.

Work and play: Meet a man who spent decades creating New York City playgrounds beloved by children.

Hall of shame: A glassy building in Manhattan is notorious for deadly bird collisions. Residents are trying to fix the problem.

Lives Lived: The Finnish statesman Martti Ahtisaari won the Nobel Peace Prize in 2008 for his diplomatic efforts to end conflict in places such as Namibia and Northern Ireland. He died at 86.

A trippy new adventure: Nintendo’s flagship star, Mario, has always been a little boring. The power-ups — mushrooms that make him grow, feathers that allow him to fly — make Mario’s games exciting. This week, the company is releasing “Super Mario Bros. Wonder,” and its power-ups turn the game into a “carnival of bizarre delights,” The Times’s Zachary Small writes. Among them: a fruit that transforms Mario into an elephant and a flower that sends him on something akin to a psychedelic trip.