President Biden spoke with President Emmanuel Macron of France on Wednesday for the first time since the United States and Britain entered into a broad new defense arrangement with Australia that scuttled a $60 billion French project to build submarines, and led France to declare its oldest ally had delivered a “knife to the back.”

The two leaders agreed to meet in Europe next month, likely on the edges of the upcoming Group of 20 summit in Italy, although White House aides said it was possible they would have a separate meeting elsewhere to underscore their resolve to repair the damage.

The White House described the conversation as “friendly,’’ just days after Mr. Macron recalled the French ambassador to the United States and suggested that Mr. Biden had done grave harm to the alliance.

While the United States has not apologized for the effort to keep France in the dark, the statement from the United States and France said that “the two leaders agreed that the situation would have benefited from open consultations among allies on matters of strategic interest to France and our European partners.”

It said that “President Biden conveyed his ongoing commitment in that regard,’’ and the countries had “decided to open a process of in-depth consultations, aimed at creating the conditions for ensuring confidence and proposing concrete measures toward common objectives.” While that statement is written in bland diplomatic language, it describes the kind of consultations that are supposed to be routine among NATO allies.

The joint announcement issued by the two countries referred vaguely to common European defense projects, but those did not appear to be new — the wording seemed to be drawn out of past NATO statements. Nonetheless, American officials were belatedly searching for special projects they could announce to reaffirm the relationship with France, including new projects in the Indo-Pacific, though some senior officials said they are concerned that anything they put together might look like a transparent, face-saving effort, especially when compared to the scope of the Australian, American and British partnership.

The core of last week’s announcement was a plan to build nuclear-powered, conventionally armed submarines, to be operated by the Australian navy, that are clearly being designed to counter China’s growing influence in the Pacific. The submarines would have a far larger range than the diesel-electric models that France was planning to build, under a deal announced in 2019.

But the true import of the new arrangement was far larger: It tied Australia firmly to the Western defense camp in challenging China, after years in which Australian leaders tried to carefully balance between their most important defense and intelligence ally in Washington and their huge customer for natural resources in Beijing. Now, after the Chinese government overplayed its hand with both political bullying and major disinformation campaigns in Australia, the country has declared itself a full partner in the Western effort to counter China’s growing influence.

But the move came as a shock to French leaders, who knew the submarine deal was in trouble but were kept in the dark about secret negotiations between Britain, the U.S. and Australia that began last spring.

A statement before the meeting from the Élysée Palace said Mr. Macron had agreed to hold the conversation at Mr. Biden’ request, and that he expected “clarifications on the American decision to keep an ally out of exchanges establishing cooperation in the Indo-Pacific.”

The statement, again reflecting Mr. Macron’s anger at what is seen in France as a betrayal, added: “We expect from our allies that they recognize that the discussions and consultations that should have taken place did not, and that this poses a question of confidence whose consequences must be reviewed together.”

The French president did not succeed in securing a reference to “European sovereignty” — a sensitive term for the United States as well as several of France’s partners in the European Union — but he did seem to gain American agreement for most of what he sought. He faces a presidential election in a little over six months and it was important for him to appear to stand firm.

The statement also called for the United States to recognize the strategic importance of French and European engagement in the Indo-Pacific, saying that the United States should fully recognize “the necessity of reinforcing European sovereignty, as well as the importance of the growing European engagement in their defense and their security.”

Mr. Macron was particularly offended, Western diplomats said, that Mr. Biden made no mention of it when they met in June during another summit meeting. The same day as that meeting, Mr. Biden also met with the British prime minister, Boris Johnson, and Australia’s prime minister, Scott Morrison, to put some finishing touches on the deal.

American officials insisted that Mr. Biden was not seeking to deceive the French, but instead was said relying on Australia to break the news to Mr. Macron. It was not up to the United States, they insisted, to disentangle Australia from its contract with France.

Mr. Biden met with both Mr. Johnson and Mr. Morrison, separately, on Tuesday.