As Gaza tips into famine and images of starving children trigger new demands for action, President Trump faces a test all too familiar to his predecessors.

Time after time, presidents have found themselves watching suffering in faraway countries with the knowledge that they could act to save innocent lives. Images of death and misery in places like the Balkans, Rwanda, Darfur and Syria, to name a few, haunted their consciences — sometimes moving them to act, but often leading to excuses.

The desperation in Gaza has emerged as such a test for Mr. Trump. By his own account, images of malnourished Gazans in the war-ravaged enclave have disturbed him enough to take action.

“I mean, some of those kids are — that’s real starvation stuff,” Mr. Trump said in Scotland on Monday. “I see it, and you can’t fake it. So we’re going to be even more involved.”

It was unclear what Mr. Trump meant by getting “more involved.” Days earlier, he had withdrawn his special envoy, Steve Witkoff, from talks between Israel and Hamas in pursuit of a cease-fire to end the Gaza war.

But Mr. Witkoff will now travel to Israel on Thursday to discuss Gaza, and Israeli news outlets reported that he might even visit a food distribution center in the territory.

Mr. Witkoff’s change of plans comes as aid groups say hunger in Gaza is reaching crisis levels. One United Nations-affiliated group said in a report this week that a “worst-case” famine scenario is unfolding, and Gaza health officials say that dozens of Gazans, including children, have died of starvation in recent weeks. Those grim facts have been driven home by gut-wrenching images of skeletal toddlers and people fighting for food.

Israeli officials reject responsibility for food shortages in Gaza, which they say are exaggerated and caused by Hamas. “There is no policy of starvation in Gaza, and there is no starvation in Gaza,” Benjamin Netanyahu, Israel’s prime minister, said. Hamas “robs, steals this humanitarian aid and then accuses Israel of not supplying it,” he added. But Hamas denies that, and Israeli military officials privately say they have found no evidence that it is true.

Such protests have not defused global anger. France announced this week that it would recognize an independent Palestinian state at the United Nations in September, and Britain said it would follow suit if Israel did not agree to a cease-fire with Hamas.

And in Washington this week, one of Mr. Trump’s fiercest Republican allies in Congress, Representative Marjorie Taylor Greene of Georgia, condemned Israel’s actions in Gaza as “genocide.”

Mr. Trump has few good options. The United States supplies Israeli, its close partner, with billions in annual military aid. Even if Hamas is the main obstacle to aid delivery, Mr. Trump lacks influence over the militant group. His only real hope is to insist that Israel, which controls Gaza’s borders, does more to clear roads and protect aid convoys.

And a long-term solution may require leveraging American aid to force Mr. Netanyahu to accept a cease-fire on terms short of his longtime demands.

Stephen Wertheim, a senior fellow in the American Statecraft Program at the Carnegie Endowment for International Peace, said the quandary is a familiar one for U.S. presidents.

“President Trump’s excuse-making over Gaza resonates with a long line of presidents who were pressured to address humanitarian catastrophes,” Mr. Wertheim said.

That pressure comes from a sense of moral duty in the country’s DNA, dating as far back as John Winthrop’s 1630 “City on a Hill” sermon, in which he told Puritan Massachusetts colonists that “the eyes of all people are upon us.”

As the United States grew in power and wealth, so did its sense of obligation to people in need everywhere. When President Herbert Hoover, a free-market Republican, ordered aid to famine-stricken Soviet Russia in 1921, he declared: “Whatever their politics, they shall be fed!” Cold War competition for global influence with the Soviet Union reinforced the instinct, on strategic grounds.

Many conservatives argue that America is not a charity, and should help people abroad only when it advances the national interest. Mr. Trump has made that argument explicit in his “America First” foreign policy, his deep cuts to foreign aid spending and his dismantling of the U.S. Agency for International Development.

Stephen Pomper, the chief of policy at the International Crisis Group, noted that a president who preaches an “America First” foreign policy has undermined an international system built over decades to prevent foreign atrocities. The United States, he said, “looks increasingly like it rejects or is indifferent to the founding principles of the order that it helped create.”

Still, the crisis in Gaza has echoes of past humanitarian crises that left presidents wringing their hands over how to respond.

President Bill Clinton took office in 1993 as a champion of human rights and international institutions. But when machete-wielding Hutu militias started to slaughter ethnic Tutsi in Rwanda in 1994, he rejected calls for U.S. action. Scarred by the deaths of 18 American soldiers on a peacekeeping mission in Somalia, Mr. Clinton feared that even modest steps could escalate dangerously. Unchecked, Hutu killers carried out the genocide of an estimated 800,000 Tutsi. Mr. Clinton later said he regretted not doing more to stop it.

Mr. Clinton also hesitated as Serbian forces slaughtered civilians in Bosnia and Herzegovina in the mid-1990s, rebuffing direct pleas from the likes of Elie Wiesel by saying the problem did not warrant risking American lives. The 1995 massacre of 8,000 men and boys at a U.N.-declared “safe area” in the Bosnian town of Srebrenica finally moved Mr. Clinton to act. A U.S.-led bombing campaign against Serbian forces led to a peace deal credited with stabilizing the region.

Stopping mass killings in the Darfur region of Sudan in the early 2000s became a campaign for activists and celebrities, including Angelina Jolie and George Clooney. But even after the State Department formally declared the atrocities there a “genocide” in 2004, President George W. Bush refused calls to deploy U.S. troops to stop it. He cited, among other things, concern about intervening “in another Muslim country” at the time of the wars in Iraq and Afghanistan.

By the time Barack Obama became president, activists and scholars — fueled by the American failure in Rwanda — had developed new legal theories to support cross-border intervention to protect victims of atrocities. Among them was Samantha Power, an influential national security aide to Mr. Obama, who helped engineer a 2011 presidential directive on the subject. “Preventing mass atrocities and genocide is a core national security interest and a core moral responsibility of the United States,” it declared.

Mr. Obama put that idea into practice in 2011, when he ordered airstrikes in Libya against government forces preparing to crush a rebellion in the city of Benghazi. Mr. Obama said he acted to avert “a massacre that would have reverberated across the region and stained the conscience of the world.”

But that supposedly limited intervention expanded into a monthslong NATO bombing campaign, and Libya collapsed into violent anarchy, leaving Mr. Obama regretting the experience. So when he was pressured again to intervene in Syria’s civil war against the country’s brutal regime, he rejected pleas for airstrikes from top officials, including Secretary of State John Kerry.

Mr. Obama did, however, order limited airstrikes in Syria in 2014 against Islamic State fighters, in part to save thousands of Yazidi people trapped on a mountain in Iraq and at risk of genocidal massacre.

“Earlier this week, one Iraqi cried that there is no one coming to help,” Mr. Obama said in an address to the nation. “Well, today America is coming to help.”

Gaza presents Mr. Trump with an especially difficult case, as it did for President Joseph R. Biden Jr.

Mr. Biden faced withering questions about his support for Israel’s military campaign, and was shouted down at public events by protesters accusing him of complicity in “genocide.” But while Mr. Biden often harangued Mr. Netanyahu to allow more aid into Gaza — usually with limited and temporary results — he never risked a full break with the prime minister over the matter.

One reason, Biden officials say, was intelligence showing that Hamas responded to signs of a potential split between the United States and Israel by hardening its negotiation position in cease-fire talks.

Mr. Biden felt enough of a responsibility — and also perhaps political vulnerability — that he resorted to dramatic displays of support for hungry Palestinians, sending military planes to airdrop supplies and ordering the construction of a $230 million pier to allow aid delivery by sea. Critics dismissed both measures as made-for-TV substitutes for putting decisive pressure on Mr. Netanyahu.

Ultimately, Mr. Wertheim said, America’s real problem in Gaza is itself.

“It’s not that other parties are engaged in atrocities and the question is whether the United States will use its righteous power to stop,” he said. “In this case, the issue is that the United States is complicit in Israel’s conduct.”