Boris Johnson has reopened the rift with Paris over the Aukus defence and security deal, urging the French to “prenez un grip about this and donnez-moi un break”, after he and Joe Biden discussed deepening the pact.

The prime minister was speaking in Washington, where he attended a dinner on Tuesday evening with the Australian prime minister, Scott Morrison, after meeting the US president at the White House.

Johnson and Biden talked about extending their cooperation through the pact to cover further issues including safeguarding human rights and promoting free markets – and ruled out inviting more countries to join.

Johnson said: “What I found on Capitol Hill was that they want to populate the agenda with all sorts of other things which matter.” He cited the need for a western rival to telecom giant Huawei, which the UK government recently decided to remove from some parts of the country’s critical infrastructure because of security concerns.

“What we need is a western technology on which we can all rely,” he said.

He added that he and Biden had been surprised at the strength of the reaction from Paris regarding Aukus – and claimed to be ready to smooth things over. “I think everybody has been a bit taken aback by the strength of the French reaction and we all want to reach out,” he said, adding: “We love the French.”

The US and UK governments believed Australia had signalled the development to France in advance, but the message appeared to have been missed in Paris. Morrison is understood to have reassured the UK prime minister at their dinner in Washington that he had carried the message to Paris as promised.

Asked whether he understood why the French were annoyed, he said: “It’s just one of those things – there are no easy ways of having these conversations – it’s a very human thing to delay until the last possible moment.”

Some Downing Street officials believe the French government has kept the public spat running so vocally in an attempt to ensure they receive the maximum compensation for the cancellation of the submarine contract.

Johnson’s latest comments came as Biden moved to soothe French fury. After a phone conversation between him and Emmanuel Macron, France announced that it would return its ambassador to the US and Biden vowed not to cut Paris out of key future defence decisions in the Indo-Pacific.

In a joint statement issued after a phone call ended a five-day standoff between the leaders, the two men agreed to meet in Europe in late October, probably at the G20 summit, to discuss how to improve consultations in future.

Macron said he would despatch his withdrawn ambassador to Washington next week, but there was no sign that the US or Australia were going to go back on their decision to work together on building nuclear powered submarines, a decision that led Canberra to cancel its A$90bn contract for the French to build diesel-based submarines.

Biden instead said the US would be supplying extra help to the French-led anti-terrorist operations in the Sahel.

The joint statement also sought to remove any suggestion that the Americans did not regard the independently minded French as unreliable partners in the efforts to constrain China in the Indo-Pacific, the chief unstated purpose of the Aukus pact.

Paris reacted with fury after the announcement of the three-way pact. When withdrawing their US and Australian ambassadors, France dismissed the UK’s role as that of a “fifth wheel”, and claiming it shows Downing Street is in “vassalage” to Washington.

Asked about the backlash on Wednesday after discussing the pact with Biden and Morrison, Johnson said: “I just think it’s time for some of our dearest friends around the world to prenez un grip about this and donnez-moi un break.

“Because this is fundamentally a great step forward for global security. It’s three very like-minded allies standing shoulder to shoulder creating a new partnership for the sharing of technology. It’s not exclusive. It’s not trying to shoulder anybody out. It’s not adversarial towards China for instance.”

Johnson has been forced to acknowledge during his US visit that a bilateral trade deal with Washington appears a distant prospect, with Biden’s priorities lying with his domestic agenda, including passing the Build Back Better bill.

Government sources have suggested the UK could bid to join the US-Mexico-Canada trade deal instead. The foreign secretary, Liz Truss, will travel to Mexico on Wednesday, and the Mexican government signalled on Tuesday it did not reject the idea outright.

Johnson’s official spokesperson has insisted striking a bilateral trade deal with the US – something the PM had previously suggested would be straightforward – remained the UK’s priority.