French President Emmanuel Macron on Tuesday called for in-depth talks with Russia, as he met US leader Donald Trump on the sidelines of a NATO summit.
"It's important to have a strategic dialogue with Russia," he said, but warned that the alliance should do so "with its eyes wide open".
Russian President Vladimir Putin had earlier indicated that Moscow was open to cooperation with NATO on common threats, including international terrorism.
But he also complained that its attempts to forge closer links had "practically been curtailed", as the alliance has expanded and strengthened its presence in former Soviet republics.
NATO for its part has criticised Russia, in particular over what it says is rising aggression in Ukraine and Georgia.
Ties with member Turkey have also been strained over its military support from Russia in the Syria conflict.
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