WASHINGTON — President Biden’s high-stakes speech in Warsaw on Saturday was crafted with the intent of throwing the full weight of the United States behind its European allies, while framing the Russian invasion of Ukraine as part of a global “battle between democracy and autocracy.”

And although the forceful denunciation of President Vladimir V. Putin’s war resonated with some leaders, it was an unprompted ad-lib that captured the attention of foreign policy experts, members of Congress and NATO allies.

“For God’s sake, this man cannot remain in power,” Mr. Biden declared, a comment that two White House officials said was not included in the president’s prepared speech.

Even as top administration officials spent Sunday walking back Mr. Biden’s remarks, the statement had already sent ripple effects throughout the world, highlighting just how powerful nine unprompted words from the president can be, particularly during a foreign policy crisis.

“I wouldn’t use this kind of words,” President Emmanuel Macron of France said in a television interview on Sunday, when asked to comment on Mr. Biden’s speech. He said he hoped to obtain a cease-fire and the withdrawal of Russian troops from Ukraine through diplomacy.

“If we want to do this, we mustn’t escalate,” he said, “neither with words nor with actions.”

Mr. Biden spent most of the speech summarizing the penalties his administration had imposed on Russia and its efforts to support refugees, while asserting that even though the United States would not send troops to Ukraine, it was prepared to defend NATO allies. Mr. Biden raised his voice when he warned Mr. Putin not to move “on one single inch” of NATO territory, a message of support for allies that the administration had intended to be one of the main takeaways from the address, according to officials.

Until Mr. Biden’s unscripted moment, the speech had largely achieved its intended goals, lawmakers, allies and foreign policy experts said. But immediately afterward, Mr. Biden’s aides worried that his surprising remark might roil some of those allies the president was determined to keep unified. The White House has tried to ensure that each step taken against Russia is in line with European allies.

Taken literally, the remark meant the United States would be reversing a policy of not pushing for regime change. Mr. Biden’s staff felt as if it had little choice but to play down the off-the-cuff comment.

“We do not have a strategy of regime change in Russia or anywhere else, for that matter,” Secretary of State Antony J. Blinken said in Jerusalem after meeting with Israel’s foreign minister, Yair Lapid. “In this case, as in any case, it’s up to the people of the country in question. It’s up to the Russian people.”

Michal Baranowski, a senior fellow and director of the Warsaw office of the German Marshall Fund who attended Mr. Biden’s speech, acknowledged that the president’s comment could be perceived as “a call for regime change.” But he said it was unlikely to lead to further escalation with Russia.

But Republican members of Congress worried that the Kremlin, which has issued propaganda claiming the United States is determined to destroy Russia, would seize on the remark.

Senator Rob Portman, Republican of Ohio, described Mr. Biden’s speech as “very strong, despite the ad-lib at the end.”

The comment “plays into the hands of Russian propagandists and plays into the hands of Vladimir Putin,” he said during an interview on NBC’s “Meet the Press.”

Indeed, Moscow was quick to respond. On Saturday, Dmitri Peskov, the Kremlin spokesman, said that it was not for Mr. Biden to decide who the Russian president should be. Vyacheslav Volodin, a senior Russian lawmaker, wrote on Telegram that neither Boris N. Yeltsin nor Mikhail S. Gorbachev, who led during the Cold War, was the target of similar comments from American heads of state.

“The reason for this behavior will be more professionally explained by psychiatrists,” Mr. Volodin said. “U.S. citizens should be ashamed of their president.”

Senator Jim Risch of Idaho, the top Republican on the Foreign Relations Committee, said Mr. Biden made a “horrendous gaffe” in an otherwise good speech.

“The administration has done everything they can to stop escalating — there’s not a whole lot more you can do to escalate than to call for a regime change,” he told CNN’s “State of the Union.”

Representative Michael McCaul of Texas, the top Republican on the House Foreign Affairs Committee, suggested the impromptu comment threatened to overshadow the discussions over how to continue to assist Ukraine in its fight against Russia.

Most of the reaction on Sunday did not seem to significantly undermine the administration’s relationship with allies that have joined in issuing sanctions against Russia.

Mr. Biden had used words “that must make Putin clearly understand that he has to stop,” Italy’s foreign minister, Luigi Di Maio, said on Saturday night. Mr. Biden made “a very clear speech, he used resolute words,” Mr. Di Maio said. “But let’s remember that on the other side, Putin uses bombs.”

Nadhim Zahawi, Britain’s education secretary, echoed the White House’s clarification, saying he was sure that both the United States and Britain agreed that the Russian people should decide how they wished to be governed.

“The Russian people will decide the fate of Putin and his cronies,” Mr. Zahawi said.

And Julianne Smith, the U.S. ambassador to NATO, suggested that Mr. Biden’s declaration was a reaction to the human cost of war he had witnessed during the three-day diplomatic trip to Europe. Noting that Mr. Biden had visited refugees before his speech in Warsaw, she said his remarks were “a principled human reaction.”

But, she insisted on “State of the Union,” “the U.S. does not have a policy of regime change in Russia. Full stop.”

Reporting was contributed by Jonathan Martin, Chris Cameron, Emma Bubola and Lara Jakes.