France and the US have made efforts to end a row which started last week with the announcement of a defence pact between the US, UK and Australia.
The Aukus pact cost France a submarine contract worth billions of dollars.
In a 30-minute phone call on Wednesday, the French and US presidents agreed to try to find a way forward.
The US acknowledged that the situation would have benefited from “open consultations”, and France agreed to send its ambassador back to Washington.
In a carefully worded joint statement, the two governments said US President Joe Biden and French President Emmanuel Macron would “open a process of in-depth consultations, aimed at creating the conditions for ensuring confidence”.
The two leaders are set to meet in Europe at the end of next month.
Aukus: The basics
What is Aukus? It’s a security pact between Australia, the US and UK. It allows for greater sharing of intelligence, but crucially it gives Australia secret technology to build nuclear-powered submarines, though not equipped with nuclear weapons
What’s the aim? Aukus is widely seen as a response to the growing power of China, and an effort to counter its influence in the contested South China Sea
Why has it angered France? Australia cancelled a $37bn (£27bn) deal with a French company building diesel-powered submarines, and, what’s more, France – a traditional Western ally – found out about the new pact only a few hours before the public announcement
Analysts have described Aukus as probably the most significant security arrangement between the three nations since World War Two.
But the pact angered the French government, with Foreign Minister Jean-Yves Le Drian describing it as a “stab in the back”.
France recalled its ambassadors to Washington and Canberra for consultations in protest over the deal.
While the ambassador to Washington will now return to his post, it is not clear if the ambassador to Canberra will do the same.
In the statement on Wednesday, Mr Biden reaffirmed the importance of French and European engagement in the Asia-Pacific region.
The BBC’s Washington correspondent Nomia Iqbal described Wednesday’s statement as a non-apology from the Americans: an apology to the French for the lack of consultation, but not for the policy itself (Aukus).
US Secretary of State Anthony Blinken and Mr Le Drian are expected to hold a bilateral meeting on Thursday on the sidelines of the UN General Assembly in New York, according to a US official.
Meanwhile, UK Prime Minister Boris Johnson said he and the other Aukus leaders were a “bit taken aback by the strength of the French reaction” and said it was time for “some of our dearest friends” to “prenez un grip”.
Analyses by Hugh Schofield, Paris Corespondent
Much trust has been lost
President Macron sent out his foreign minister to do the dirty stuff. Presumably he told Jean-Yves Le Drian not to feel too diplomatically restrained – to let the anger out. Hence the minister’s remarks about “lying” and stabs in the back.
And hence the return accusations of French “petulance” and toys thrown out of prams.
The division of labour inherent in the French system means that the president is now free to rise above the name-calling and – in a true embodiment of French national interest – take the high road to reconciliation.
With the Americans, anyway. The Australians will have to wait.
Washington played along by admitting things could have been handled differently, giving a nod to European defence and agreeing to boost support in North Africa. The French ambassador goes back to Washington next week. They’re talking again, but much trust has gone.
Source: BBC