When the White House invited Muslim community leaders for a dinner this week celebrating the holy month of Ramadan, the responses started coming in fast: Decline. Decline. Decline.

Many of the invitees, distressed over President Biden’s support for Israel’s war in Gaza, said they would not attend an iftar meal with the president on Tuesday evening while so many Palestinians were under siege.

“How can we talk to you about famine and starvation over bread and steak?” said Dr. Thaer Ahmad, a Palestinian American doctor who was in Gaza in January.

The moment epitomized just how problematic the war in Gaza has become for Mr. Biden, who is increasingly critical of Israel but still resisting calls from within his party to set conditions on weapons sales to the country.

The White House pivoted quickly as it became clear that the Ramadan event would be controversial, holding a pared-down meal just for staff members and a separate meeting for Muslim community leaders like Dr. Ahmad.

The meeting, which lasted for more than an hour, was attended by Mr. Biden; Vice President Kamala Harris; Jake Sullivan, the national security adviser; and other senior officials. Three doctors who had recently treated patients in Gaza were among those who spoke to the president.

More than 32,000 people have been killed in the war, according to the Gazan health authorities.

Dr. Ahmad said he told Mr. Biden that Israel’s impending ground invasion of Rafah would be a “blood bath and a massacre.” He also handed the president a letter from an 8-year-old girl in Gaza who lost her entire family in the war.

“We in Rafah are suffering a lot because we live in a very small tent and the tank can enter the tent and run me over,” the girl wrote in the letter, which was obtained and translated by The New York Times.

The letter continued: “We don’t want massacres and suffering. We want safety, to live like the rest of the world’s children. Please, Biden, stop this war, it’s enough, stop this war please.”

After speaking for about six minutes, Dr. Ahmad told the president he was leaving.

“I said, ‘Out of respect for my community, and out of respect for the many people who are grieving, and who are in a lot of pain, I have to walk out of this meeting.’”

He said Mr. Biden responded that he understood.

“Part of me wanted to express the frustration that the entire community has, the anger and the resentment,” Dr. Ahmad said. “But also part of me wanted to get up and walk out on the decision makers, and give them an idea of how it feels to have somebody walk away from them.”

It was a far cry from a celebration last year at the White House marking the end of Ramadan, which drew hundreds of community leaders, White House staff and politicians who snacked on hors d’oeuvres and took selfies with the president. One attendee shouted “We love you!” to Mr. Biden before he started speaking.

This year, as the Biden administration hosted its pared-down meeting and meal, protesters knelt outside the White House in prayer.

Tuesday’s meeting with Muslim leaders and community members was among several the administration has held in recent months, both internally with staff and with outside groups, as it has tried to calm widespread indignation over the war.

Mr. Biden’s stance has angered crucial constituencies in Mr. Biden’s base, including young people, Black voters and progressives.

Karine Jean-Pierre, the White House press secretary, declined on Wednesday to comment on the details of Tuesday night’s meeting, saying it was private. But she said that the president knows that it was a “deeply painful moment for many in the Arab and Muslim communities.”

“The president also expressed his commitment to continue working to secure an immediate cease-fire as part of the deal to free the hostages and significantly increase humanitarian aid into Gaza,” she said. “And the president made clear that he mourns the loss of every innocent life in this conflict — Palestinian and Israeli.”

When asked about Dr. Ahmad walking out, Ms. Jean-Pierre said the president respected the right to peacefully protest.

Salima Suswell, the chief executive officer of the Black Muslim Leadership Council, who also attended the meeting, said she told Mr. Biden about the “moral dilemma” some members of the Black Muslim community feel supporting him because of the war in Gaza.

“Black people identify and somewhat relate to this issue that involves oppression and the dehumanization of people,” Ms. Suswell said. “Our ancestors lived through 400 years of it.”

She said Mr. Biden said he was committed to the Black community.

Ms. Suswell, who stayed for the duration of the meeting, said attendees shared their experiences from the ground in Gaza. One of the doctors passed around photos of children there, she said.

Both Mr. Biden and Ms. Harris expressed that they wanted the war to end as soon as possible. When asked about calling for an immediate and permanent cease-fire, Mr. Biden said that Israel would push back because of concerns about the hostages.

“They both said, ‘We don’t want to see this war continue,’” Ms. Suswell said.

Hiba Yazbek contributed reporting from Jerusalem.