Acting US Defence Secretary Patrick Shanahan last week sent a letter telling Turkey that it had to renounce the S-400 system by July 31, or Turkish pilots training on the F-35 fighter jet programme would be expelled from the United States.

The letter said agreements with Turkish firms subcontracted for manufacturing parts of the stealth warplane would also be cancelled.

In a phone call, Defence Minister Hulusi Akar told Shanahan that the letter's wording was "inappropriate and not in line with the spirit of (NATO)", according to a ministry statement.

They reportedly discussed the F-35 programme and agreed that talks would continue.

Turkey's push to buy the S-400 system has strained relations between the NATO allies, with the US worried it could give Russia access to sensitive technical knowledge if operated alongside its fighter jets.

It faces potentially crippling economic sanctions if it goes ahead with the purchase.

But Turkey has repeatedly stated it is a "done deal" and Akar said last month that Turkish personnel had already been sent to Russia for training on the S-400.

"No one can give Turkey an ultimatum," Foreign Minister Mevlut Cavusoglu told reporters on Thursday.

He repeated an offer to set up a joint working group to resolve US concerns, saying President Donald Trump looked favourably on the idea but that it was rejected by "some institutions" in the US.

President Recep Tayyip Erdogan on Wednesday said he hoped to persuade the US not to exclude Turkey from the F-35 programme.

Turkey has said it will formally respond to Shanahan's letter in the coming days.

The US "delivered" four F-35s to Turkey in June 2018, but kept the planes in the country, officially to train the Turkish pilots.