London (AFP) - US President Donald Trump and Emmanuel Macron exchanged fire over the future of NATO on Tuesday, as the French leader attacked Turkey and demanded the alliance rethink its strategy.

The three-way battle overshadowed the start of the alliance's 70th anniversary summit in London, threatening to derail efforts to show unity in the face of Russia and China.

In recent weeks Macron has tried to shake up the agenda of the meeting by demanding a review of NATO's "brain dead" strategy, but Trump -- who arrived boasting that he had forced members to boost defence spending -- hit back hard.

"I think that's very insulting," Trump said of Macron's assertion last month that NATO is rudderless and should focus more on Islamist terrorists and on re-opening a strategic dialogue with Russia, branding it a "very, very nasty statement".

"Nobody needs NATO more than France," he warned. "It's a very dangerous statement for them to make."

Trump later softened his tone at a joint appearance with Macron, but the French leader stood by his statement, and accused Turkey of working with extremists in Syria.

"The common enemy today are the terrorist groups, as we mentioned, and I'm sorry to say that we don't have the same definition of terrorism around the table," Macron said.

He noted that Turkey has attacked the Kurdish militia that backed the allies against the Islamic State and accused Ankara of working with "ISIS proxies".

Macron and Turkish President Recep Tayyip Erdogan later came face to face at four-way talks with Germany's Chancellor Angela Merkel and Britain's Prime Minister Boris Johnson, and all 29 NATO leaders had dinner with Queen Elizabeth II in Buckingham Palace.

Merkel said she was "relatively optimistic" after the meeting, but Macron warned that "not all clarifications were obtained and not all ambiguities were resolved".

"There are disagreements, choices that are not the same but there is a need to move forward. I'm a pragmatist," he said.

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Erdogan has threatened to hold up NATO efforts to beef up the protection of the Baltic republics against Russia, unless the other allies declare the Kurdish militias who fought with US and French forces against the IS group in northeast Syria "terrorists".

NATO has mooted a plan to bolster the defences of Poland, Estonia, Lithuania and Latvia against a potential attack from Russia, though details remain unclear.

Polish President Andrzej Duda played down the dispute, saying he believed "a good solution" would be found.

But he too weighed in on Macron, urging him to stop carping about NATO and come up with "concrete propositions" for how to improve the alliance.

- Not paid up in full -

NATO Secretary-General Jens Stoltenberg renewed his own criticism of the French leader's remarks, saying allies "should never question the unity and the political willingness to stand together and to defend each other".

Trump defended Stoltenberg, boasting that NATO members have massively increased their defence spending thanks to his pressure.

But the president then reiterated his long-standing complaints about European spending.

"When I came in, I was angry at NATO, and now I've raised $130 billion," Trump said, referring to the sum Stoltenberg says Canada and European members will have added to defence budgets by next year.

"And yet you still have many delinquent -- you know I call them delinquent when they're not paid up in full," he said.

Only nine of NATO's 29 members have reached the target agreed at the 2014 summit to spend two percent of their GDP on defence before 2024.

Trump cited in particular Germany as falling short, spending only 1.2 percent.

Russian President Vladimir Putin said Moscow was open to cooperation with NATO against joint threats such as terrorism.

In a move likely to unsettle eastern European NATO allies that feel threatened by Moscow, Macron appeared receptive to the idea, calling for a "strategic dialogue" with Russia.

- Where next? -

The substance of the summit is thin, with only one three-hour session planned, where leaders are expected to sign off on a set of decisions already taken by NATO foreign and defence ministers.

These include making space a full domain of conflict -- alongside land, sea, air and cyber space -- as well as acknowledging the "challenges" posed by China for the first time.

They are expected to approve a new report on how the alliance should approach China and its growing international assertiveness.

"We have now recognised that the rise of China has security implications for all allies," Stoltenberg said.

What is likely to be more significant in the longer run is the fallout from Macron's broadside, in which he complained NATO talks too much about money and not enough about strategic priorities.

In response, Germany has suggested setting up an expert panel to look at how NATO can be adapted to address political questions more effectively.