President Biden will travel to Israel on Wednesday to show solidarity with America’s closest ally in the Middle East, in a wartime trip to bolster the country’s resolve to eradicate Hamas but also to urge limits on what seems bound to be a casualty-filled ground invasion of the Gaza Strip.

It will be a trip fraught with risks, both political and physical.

The White House announced the visit on Monday evening after Mr. Biden met with his top intelligence officials and his closest advisers in the Oval Office to debate whether to accept the invitation that Prime Minister Benjamin Netanyahu extended over the weekend.

In a briefing to reporters Monday night, John F. Kirby, a spokesman for the National Security Council, said Mr. Biden would focus on “the critical need for humanitarian assistance to get into Gaza, as well as the ability for innocent people to get out.”

He said the president would have meetings in Tel Aviv and in Amman, Jordan, with the leaders of Jordan, Egypt and the Palestinian Authority.

While Mr. Biden and Secretary of State Antony J. Blinken have backed the overthrow of Hamas, they have also stressed to Mr. Netanyahu’s government that once Israel is seen blowing up buildings and triggering Palestinian casualties, public sentiment around the world could change dramatically. It would focus less on the Oct. 7 terrorist attack, with its scenes of burned bodies and massacred children, and more on the brutality of the response.

“We obviously don’t want to see any additional civilian suffering,” Mr. Kirby said, though he added that there were no conditions being put on the arms and other aid being shipped to Israel.

Before the announcement, two administration officials, noting the pro-Palestinian marches in Europe, in New York and on some American college campuses, said in interviews that they could already sense the narrative shifting. They spoke on the condition of anonymity to discuss the administration’s internal assessments.

Mr. Biden’s visit is an extraordinary show of support to Israel in the midst of war, akin to Mr. Biden’s brief trip to Ukraine in February to shore up international support for President Volodymyr Zelensky. And just as Mr. Biden’s trip to Kyiv came as Ukraine was on the cusp of a major military operation, the visit to Jerusalem comes as hundreds of thousands of Israeli troops are poised to fight their way through the jammed urban landscape of Gaza to carry out Mr. Netanyahu’s vow to eliminate Hamas.

The security risk of such a trip was clear on Monday when sirens warning of incoming rockets or missiles went off while Mr. Blinken, who was in Israel for his second visit in a week, was meeting at a military base with Mr. Netanyahu and his war cabinet. Mr. Blinken and his hosts were rushed to a bunker and sheltered there for five minutes before resuming their discussions. (There was a similar warning when Mr. Biden was touring a few blocks of Kyiv with Mr. Zelensky in February.)

But the physical risks in Tel Aviv were considered low enough, Mr. Kirby said, that “it was deemed appropriate that we can talk about it beforehand.” The trip to Kyiv, where there were no American forces present to back up the Secret Service, was kept secret.

Mr. Biden has often said he feels very comfortable in Israel, as was evident during his one visit as president in July 2022. Mr. Netanyahu was out of power at the time, which was fine with Mr. Biden’s team. The administration has been in constant conflict with the Israeli leader over his efforts to strengthen his power by overhauling the judiciary, and the efforts of his far-right coalition to expand settlements in disputed lands.

Now, though, Mr. Netanyahu is at the head of a unity government that has come together specifically to prosecute the war, combining with the former Defense Minister Benny Gantz and his centrist party. Mr. Biden’s aides are hoping that the central role for Mr. Gantz, a former general who served in the Israel Defense Force for 38 years, will change the dynamic of their discussions.

But Mr. Gantz campaigned against Mr. Netanyahu in 2019 by portraying himself as a hard-liner, boasting that when he was chief of staff, the top military post, “parts of Gaza were sent back to the Stone Age.” He was also accused of unnecessary civilian casualties.

The political risks for Mr. Biden are difficult to measure. In his first significant public effort to urge caution on Israel, Mr. Biden warned on “60 Minutes” on Sunday that “I think it’d be a big mistake” for Israel to occupy Gaza again, a step Israeli officials say they have no intention of taking. But they have not explained who would run the Gaza Strip in the absence of Hamas, or how they could keep a similar group from arising from the ashes of Gaza City.

He also cautioned that “there needs to be a Palestinian Authority; there needs to be a path to a Palestinian state.” He and others in the administration are repeating, with increasing frequency, that most Palestinians in Gaza do not support Hamas, which has controlled the slice of land now for more than 16 years.

Israeli officials are offering assurances that they will work to limit the number of civilian deaths. They blame Hamas for telling Gazans to stay in place, rather than comply with Israeli warnings to evacuate to the south — where Israel is already attacking with missiles. But several American officials have noted that the reservists called back into service by Israel largely have little training in urban warfare and are likely to shoot at anything that moves.

The visits by Defense Secretary Lloyd J. Austin III and Mr. Blinken, and now Mr. Biden, are partly intended to force Israeli officials to think about how to go into Gaza without getting stuck there — and without being seen as indifferent to the Palestinian civilians. So far, according to one official who has been involved in the talks, Israeli officials have said that it is too early to think about Gaza’s future because Hamas must be eliminated first.

“Biden believes he has the moral authority here,” said Thomas R. Nides, who served as Mr. Biden’s ambassador to Israel until he resigned over the summer. “He has stood up for the state of Israel. He believes they are right to be dismantling Hamas. But he wants to show he stands for humanity, too.”

The result is that Mr. Biden’s aides have been trying to buy some time. Keeping American officials in Jerusalem, they note, forces Israeli officials to keep discussing their plans. Assuming that the White House makes a delay of the invasion a condition of coming, a presidential trip could give the Israelis some more time to prepare for any operation and allow more Gazans to evacuate.

While Mr. Biden’s administration is working to alleviate the humanitarian crisis in Gaza, so far it has not criticized Israel’s moves to cut off electricity and food there. But Arab leaders have protested to American officials that the blockade amounts to collective punishment and is illegal under the laws of war.

Mr. Blinken’s effort to create an escape hatch for the Palestinians — or even Americans trapped in Gaza — has so far been unsuccessful. In a long meeting on Sunday, Mr. Blinken had not persuaded President Abdel Fattah el-Sisi of Egypt to open the one gate in the south of Gaza and allow Palestinians to escape to the Egyptian desert, away from the fighting. The public portions of Mr. Blinken’s encounter with the Egyptian leader were tense, with Mr. Sisi accusing the United States and its allies of being more shocked by the murder of Israelis than a decade and a half of Palestinian confinement to Gaza.

“Yes, it is true what happened over the past nine days was very difficult and too much, and we unequivocally condemn it,” Mr. Sisi told Mr. Blinken on Sunday. “But we need to understand that this is the result of accumulated fury and hatred over four decades, where the Palestinians had no hope to find a solution. Many people ask: Is this the right time to speak about this or only to try to find a way out of the current crisis?”

Unlike other presidents who have urged restraint on Israel during past conflicts, Mr. Biden has emphasized that Israel has every right to defend itself. A visit, said Richard Fontaine, the head of the Center for a New American Security, “would be a further embrace and a reaffirmation that regime change in Gaza is the right choice.”

As in Ukraine, Mr. Biden has said he will support the effort with everything short of sending Americans in with Israeli forces.

Mr. Biden has dispatched American warships and aircraft to the region to deter Iran and its proxy, Hezbollah, from widening the war. The two carrier groups, one named for President Gerald R. Ford and the other for Dwight D. Eisenhower, have been positioned so they could hit Hezbollah missile sites in Lebanon or elsewhere, if a second front opens up. A senior official said Mr. Biden would have to issue specific orders for the carrier groups to use their firepower, but he has reportedly indicated he is willing to do so.

Meanwhile, American military officers with vivid memories of the fights for Falluja in 2004 — a six-week struggle against Iraqi insurgents that was some of the most intense urban combat of modern times — have been conveying the lessons of that battle, and one in Mosul, to their Israeli counterparts.

As a matter of domestic politics, the trip provides a pretty straightforward counterpoint to former President Donald J. Trump. Mr. Trump has described himself as Israel’s strongest supporter while in office. But he has criticized Mr. Netanyahu in the days since the Hamas attack, apparently because the prime minister acknowledged Mr. Biden’s election when it became clear Mr. Trump had lost.

Mr. Trump initially praised Hezbollah as “very smart” after the massacre. He condemned the terrorist group only after he was criticized later.

The Lebanese militant group clashed with Israeli forces in the days after the Hamas attack, intensifying concerns that the country could be drawn into a conflict on a second front.

Mr. Trump’s “very smart” comments were similar to a line he used about Vladimir V. Putin after the invasion of Ukraine.

“This is a way of defanging the do-you-support-Israel issue, which Republicans used to criticize Obama and then became a Trump talking point,” said Daniel Byman, a professor at Georgetown University. “This, politically, stands in contrast with Trump’s criticism of Netanyahu.”

Edward Wong contributed reporting from Tel Aviv.