"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 expressed 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.

The warm words from Biden and apparent boost for the delayed F-16 purchases came a day after Turkey surprised fellow NATO members by suddenly dropping weeks of opposition to the Finland and Sweden applications to join the alliance, where unanimous consent is required for enlargement.

On Tuesday, a senior US official stressed that Turkey had not asked for any "particular concession" to give its green light.

Turkey is an important NATO member in a strategically sensitive location, but it has had often tense relations with its European partners and Washington, which is the alliance's main military force.

A plan to equip Turkey with state-of-the-art US F-35 stealth fighters fell through after Turkey bought Russia's S-400 anti-aircraft missile system, something Washington saw as potentially threatening the security of the F-35 programme.

Turkey next set out to buy new F-16 fighter jets, as well as upgrades for its existing, but outdated fleet of the same planes. However, that deal is also on hold and there has been speculation that Turkey was holding up the NATO accession bids of the two northern European countries to try and leverage concessions.

"There's nothing the United States offered in direct connection with this," the US official said after Turkey ended that obstruction.

"Nothing about Turkish requests to the United States was part of this agreement. This is an agreement strictly among the three countries -- Turkey, Finland, Sweden. The United States is not a part of it."

In brief comments at the start of Wednesday's meeting with Erdogan, before reporters had to leave the room, Biden also praised the Turkish leader for doing a "great job" on trying to find ways to get Ukrainian wheat out of the country to markets.

Russia's invasion, including the conquest of swathes of rich agricultural land and coastline, has severely disrupted the flow of grain to international clients, helping trigger an increasingly severe food supply crisis.

The United States and allies say Russia is using food insecurity as a weapon of war, something Moscow denies.

"I'd like to talk to you about those things," Biden said.

In comments through a translator, Erdogan said he was pleased with the outcome of the Madrid summit.

"Thanks to our efforts, we believe that we will be able to go back to our countries with our hands full and with full satisfaction," he said.

Regarding the food crisis, Erdogan said "there are countries deprived of the grains and we will open corridors and we will allow them to have access to the grains."