The White House national security advisor has said the US is "very sympathetic" toward France in its dispute with Turkey over a naval standoff in the Mediterranean Sea.

The row has also, in a way, exposed NATO's struggle to keep order among its ranks, demeaning US leadership under President Donald Trump.

"NATO allies shouldn't be turning fire control radars on each other. That's not good," national security adviser Robert O'Brien told reporters in Paris on Wednesday.

"We are very sympathetic to the French concerns," O'Brien said, while acknowledging differing accounts of what happened. "We're taking it very seriously."

He added Trump was available to help defuse tensions, thanks to his personal relationships with Turkish President Recep Tayyip Erdogan and French President Emmanuel Macron.

According to French accounts of the June 10 incident, the frigate Courbet was illuminated by the targetting radar of a Turkish warship that was escorting a cargo ship.

France said it was acting on intelligence from NATO that the civilian ship could be involved in trafficking arms to Libya. The Courbet was part of the alliance's operation Sea Guardian, which helps provide maritime security in the Mediterranean.

Turkey's foreign minister accused France of lying, and Turkey's ambassador to France said the French navy was harassing the Turkish convoy.

Macron has also accused Turkey of flouting its commitments by ramping up its military presence in Libya and bringing in jihadi fighters from Syria.

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US backs France in stand-off with Turkey over warships - WION