When President Biden said he was “outraged and heartbroken” about the killing of seven World Central Kitchen aid workers in Gaza, his forceful language raised a natural question: Would this strike, even if a tragic error, lead him to put conditions on the weapons he sends to Israel?

So far, the White House has been silent on whether Mr. Biden’s anger is leading to a breaking point with Prime Minister Benjamin Netanyahu, with whom every interaction has been tense. But in public, at least, Mr. Biden has limited his responses to ever more indignant declarations.

Launching a bombing campaign on the southern city of Rafah would cross a “red line,” Mr. Biden has insisted, without laying out the consequences. The attack on the World Central Kitchen convoy is more evidence that Israel “has not done enough to protect aid workers,” he said on Tuesday, without specifying how its behavior should change.

“I hope this will be the moment where the president changes course,” said Senator Chris Van Hollen, Democrat of Maryland and one of Mr. Biden’s most enthusiastic supporters, who pressed for months to place conditions on the arms the United States supplies. “Netanyahu ignored the president’s requests, and yet we send 2,000-pound bombs with no restrictions on their use.”

“We shouldn’t send bombs first and hope for some assurances later,” he concluded.

Conditions on how American arms are used are usually standard fare, some imposed by Congress and others by the president or secretary of state. Ukraine, for example, is not permitted to shoot American-made weapons into Russia, and even though it has generally complied, there is still debate within the administration about whether to give more powerful missiles to Kyiv if an aid package ever passes Congress.

But Israel has always been the exception. Even when Senator Chuck Schumer, Democrat of New York and the majority leader, gave an impassioned speech urging new elections in Israel — a clear effort to oust Mr. Netanyahu — he declined to call for limits on arms. When pressed the next day, Mr. Schumer said he did not even want to discuss the topic.

There are other steps Mr. Biden could demand. For example, the United States could insist that aid convoys be escorted by the Israel Defense Forces, or that nearby Israeli military units remain in constant communication with the aid providers, an issue two U.S. senators raised to Mr. Netanyahu in February.

The prime minister, one participant said, told an aide present at the meeting that he thought the problems surrounding safe passage for food and medicine had already been addressed. But he assured the senators, Chris Coons of Delaware and Richard Blumenthal of Connecticut, both Democrats, that he would bring up the issue with his military commanders.

The strike on Monday suggests that those issues were never fully resolved.

Pressed by reporters on Wednesday about Mr. Biden’s thinking on the subject, John F. Kirby, a White House national security spokesman, pointed reporters to the president’s statement condemning the strike on the aid workers.

“I think you could sense the frustration in that statement yesterday,” Mr. Kirby said.

On the day of the strike, Mr. Biden’s national security adviser, Jake Sullivan, and Secretary of State Antony J. Blinken held a previously scheduled discussion with Israeli officials via secure video.

Mr. Kirby said the Americans urged the Israelis to have a comprehensive plan to evacuate the 1.5 million refugees in the Rafah region. He also said conversations would continue about “what Rafah looks like now and what their intentions are for operations against those Hamas battalions that are still there.”

While Mr. Kirby did not say so, officials familiar with those discussions said the United States still feared the Israelis did not have a credible plan for a comprehensive evacuation — a process they believe could take months. But the officials noted that Mr. Netanyahu has not yet launched the Rafah attacks, perhaps because Israeli forces are nowhere near ready, or perhaps because of the American pressure.

There have been other moments in the six months since Hamas’s Oct. 7 terrorist attacks when the United States has hit a wall in dealing with Mr. Netanyahu, and where declarations of common goals could not hide the fact that the two countries are deeply at odds about how to conduct the war.

But it is possible that the attack on the World Central Kitchen convoy, one of the most successful efforts to avoid famine in Gaza, was a breaking point for Mr. Biden.

He personally knows the famed Spanish American chef behind the operation, José Andrés, whose restaurants in Washington are regular haunts of the city’s power brokers. Mr. Biden called the chef on Tuesday, shortly before Mr. Andres published a guest essay in The New York Times declaring that “Israel is better than the way this war is being waged.”

“It is better than blocking food and medicine to civilians,” he continued. “It is better than killing aid workers who had coordinated their movements with the Israel Defense Forces.”

But Mr. Biden consistently stops short of openly breaking with Mr. Netanyahu, a confrontation he believes will only make the prime minister more difficult to handle, aides say. The result is that Mr. Biden is in a box, criticized by the progressive wing of his party — and increasingly by moderates — for acting too cautiously, and unwilling to be perceived as limiting Israel’s ability to defend itself.

In fact, it left a sour taste among some of Mr. Biden’s critics that the president’s most visceral expression of anger at Israel’s military campaign came over the killing of seven foreign humanitarian workers rather than over the deaths of the many thousands of Palestinian civilians that preceded them.

“To me, the language of outrage, it’s noticeable because it’s the furthest he’s gone in his language but it’s also noticeable that he’s only gone this far when it’s Western aid workers,” said Yousef Munayyer, the head of the Palestine-Israel program at the Arab Center Washington D.C. “Of course it’s outrageous,” he added of the latest incident, “but these kinds of strikes, we’ve seen them repeatedly and the White House does not seem to be outraged over them.”

Mr. Munayyer said the disparity was particularly striking given Mr. Biden’s reputation for personal compassion. “He has presented himself as this empath-in-chief; that is his great quality,” Mr. Munayyer said. “And yet when it comes to Palestinian life, he just seems incapable of showing empathy to Palestinians.”

In recent weeks, Mr. Biden has tried to divorce his pressure campaign on Israel from his power, if he chose to use it, to limit the country’s arms supplies. Indeed, some veteran diplomats doubted this would be the moment that shifted Mr. Biden’s approach, despite his strong words.

“One would think ‘outrage’ would translate into a strong policy response, but so far, that does not appear to be the case,” said Daniel C. Kurtzer, a former ambassador to Israel. “Israeli apologies notwithstanding, this attack will substantially increase pressure on aid deliverers and thus worsen the humanitarian distress.”