President Joe Biden met his Turkish counterpart Recep Tayyip Erdogan on Wednesday and thanked him for dropping opposition to the entry of Finland and Sweden into NATO, with the US also signaling support for Turkey's plan to buy F-16 warplanes.

"I want to particularly thank you for what you did putting together the situation with regard to Finland and Sweden," Biden told Erdogan at a meeting on the sidelines of the NATO summit in Madrid.

A senior US official signaled strong backing for Turkey's wish to upgrade its air force with new F-16 fighter planes and improvements to its existing older fleet.

"The US Department of Defense fully supports Turkey's modernization plans," Celeste Wallander, assistant secretary of defense for international security affairs, told reporters.

"Turkey is a highly capable, highly valued, strategic NATO ally and Turkish defence capabilities, strong Turkish defence capabilities, contribute to strong NATO defence capabilities," she said.