At the United Nations’ annual gathering of world leaders this week, President Biden and Secretary of State Antony J. Blinken spoke ambitiously about international cooperation and a new diplomatic approach for a post-Trump America.

Mr. Biden’s U.N. speech on Tuesday depicted an America whose withdrawal from Afghanistan had turned a page on 20 years of war after the attacks of Sept. 11, 2001. Now, he said, the United States is embarking on a new era of cooperative diplomacy to solve global challenges, including climate change, the pandemic and rising authoritarianism.

The comments offered a grand homage to internationalism and a stark contrast to Mr. Trump’s undiplomatic bluster. But the speech also came amid growing complaints that some of Mr. Biden’s signature policy moves carried echoes of Mr. Trump’s approach.

French officials openly likened the Biden administration to Mr. Trump’s in the recent failure to warn them of a strategic deal with Britain and Australia that they said muscled them out of a submarine contract, though Mr. Biden soothed the strained relations to some extent in a call with President Emmanuel Macron on Wednesday. Mr. Blinken met in New York with his French counterpart on Thursday.

The flare-up with Paris might have been dismissed as an isolated episode but for its echoes of complaints by some NATO allies that Mr. Biden had withdrawn from Afghanistan without fully consulting them or alerting them to Washington’s timeline. Mr. Trump was notorious for surprising longtime allies with impulsive or unilateral actions.

In a fiery address to the United Nations General Assembly on Wednesday, President Ebrahim Raisi of Iran suggested that there was little difference between Mr. Biden and his predecessor, invoking their respective foreign policy slogans: “The world doesn’t care about ‘America First’ or ‘America Is Back.’”

Loren DeJonge Schulman, who worked at the National Security Counsel and the Pentagon during the Obama administration, dismissed such parallels.

“It’s absurd on its face for allies, partners or anyone to think that there is any continuity between Trump and Biden in terms of how they view allies, negotiate internationally or approach national security,” she said. “It’s a talking point, and it’s a laughable one.”

But even some of Mr. Biden’s allies admit what his foes assert: that global concerns about whether Mr. Trump, or someone like him, might succeed Mr. Biden and reverse his efforts are valid.

In response to the ambitious targets Mr. Biden offered in his address to reduce global carbon emissions, an editorial in Beijing’s hard-line Global Times newspaper raised an all-too-familiar point for Biden officials: “If the next U.S. administration is again a Republican one, the promises Biden made will be very likely rescinded.”

The Iranians made the same point about Mr. Biden’s potential return to the 2015 nuclear deal that Mr. Trump abruptly exited.