Keir Starmer has admitted that he has to “turn things around” after the resignation of the defence secretary, John Healey, in an escalating row over military spending that has prompted recriminations across Whitehall and concern from the US.

Downing Street and the Treasury traded blows with allies of Healey on Friday. No 10 expressed dismay that the Ministry of Defence (MoD) had wanted £18bn to plug funding gaps in major projects, while those close to the former defence secretary accused Starmer of failing to acknowledge the deterioration in global security.

The prime minister, speaking to the BBC, promised again to fight any leadership challenge from Andy Burnham and fended off fresh accusations that he had underestimated the need to spend more on defence.

Starmer, however, said anybody who replaced him would face the same set of difficult tradeoffs as he justified his decision to restrict funding on the defence investment plan at a time when his premiership is in jeopardy.

“I would just gently say this: that whoever is prime minister is going to face the same prevailing winds as I am facing. None of that is going to change,” Starmer said.

No 10 sided with the Treasury on Friday to complain that it had been surprised by an MoD demand for more cash to fund major projects after the publication of the strategic defence review last year.

But allies of Healey hit back, saying the geopolitical environment had worsened since the US-Israeli attack on Iran, while Starmer had committed the UK to potential peacekeeping missions in Ukraine and the strait of Hormuz.

“Anyone with a brain can see that the world has changed in the past year. Demands on defence have risen by the day since the strategic defence review,” an ally of Healey said on Friday. “That’s why the PM was right to sign the UK up to 3.5% after the strategic defence review at Nato,” they added.

Healey quit on Thursday, accusing Starmer of putting the country’s security at risk and being unable to stand up to his chancellor, Rachel Reeves. No 10 and the Treasury offered to plug £13.5bn of an £18bn deficit in spending on defence projects.

Healey also revealed that Starmer had only offered to increase defence spending to 2.68% of GDP by 2030, about £25bn below the Nato target of spending 3.5% by 2035, as agreed by the prime minister a year ago.

Government sources said there was unhappiness that the MoD had told ministers it had a major shortfall in its budgets during an already agreed spending review – and was wanting commitments in advance after 2029.

That was amplified by the Treasury. “The question is, how did we get from being told the defence review was fully funded to being told there was an £18bn black hole? We still don’t have the answer to that,” a Treasury source said.

There were also signs of concern in the Trump administration. Elbridge Colby, the influential US undersecretary of defence, cited Healey’s resignation letter and appeared to call for the UK to spend more.

“There is again a great need for more British military strength in this critical time,” he said in a social media post. “We urge the UK to meet that need with urgency, scale, and determination.”

On Friday, the New York Times reported that the US also wanted to reduce its military presence in Europe, cutting the number of F-15 and F-16E fighter jets from 150 to 100, as it expects the UK and other European members of Nato to take the lead on defending the continent from Russia aggression.

Next week, Starmer will face Donald Trump and other G7 leaders at a summit in France, where he will have to deal with the fallout from the crisis. Most G7 countries are partners with the UK on major defence projects.

However, there was no immediate sign of a turnaround on defence spending. Starmer met Healey’s replacement, Dan Jarvis, on Friday morning and Richard Knighton, the chief of the defence staff, to discuss the budget crisis.

It had been planned to publish the defence investment plan on Monday, but this has been delayed until close to the start of the Nato summit in Ankara, Turkey, at the beginning of July, giving Jarvis a limited opportunity for input.

“Jarvis inherits what the MoD considers an inadequate settlement,” said Matthew Savill, a defence policy specialist with the Royal United Services Institute thinktank. “At best, he will have some influence on the prioritisation of programmes.”

Jarvis spent his first day in the job visiting a drone testing site in Swindon, which Starmer had been due to visit until Healey resigned. The planned public event took place behind closed doors, with employees told not to mention the defence investment plan or the crisis of the past 24 hours.

The new minister, a veteran of the Parachute regiment, said “the defence of our nation is the first duty of government”, in his only public remarks. In Swindon he told those behind closed doors that there were “significant challenges ahead” as well as “great opportunity”.

Al Carns, the armed forces minister, also resigned late on Thursday. Speaking to the BBC on Friday morning, Carns accused the government of not spending enough money on the military and spending on the wrong weapons.

With Burnham increasingly expected to win next Thursday’s Makerfield byelection and return to Westminster, many Labour MPs see a leadership challenge as imminent. It could also involve the former health secretary Wes Streeting, who quit Starmer’s government last month in the wake of terrible election results for Labour.

Asked if he would lead Labour into the next general election, Starmer replied: “Well, that’s what I want to do. I recognise that, you know, I’ve got to turn things around. We had a very bad set of elections.”

The prime minister said he had overseen “the biggest sustained increase in defence spending since the 1980s”, adding that every government department had submitted cuts to non-frontline spending to help finance the spending plan. Previously agreed budgets in other departments were trimmed by 1% to make up the shortfall.

He criticised the idea that balancing such decisions was simple. “Very many people, very often sitting outside of government, give the impression that there is lots of easy decisions that can be taken. There are no easy decisions.”

Under Starmer, Labour committed to lifting defence spending to 2.6% of GDP by 2027, paying for it by cutting the overseas aid budget. But the MoD is concerned that there is no plan to go progressively by the end of the parliament in 2029, meaning that achieving the longer-term 3.5% target becomes unrealistic.