"It is out of the question to leave the S-400s and go towards the Patriots when we are at this point" of strengthening relations with Russia, Erdogan told Turkish journalists on board his plane after talks with US President Donald Trump Wednesday.

"We said 'But we would buy the Patriots too'. However, we will also have the S-400," he added, quoted by Hurriyet daily.

Erdogan had earlier in the interview spoken about Turkey and Russia's improving bilateral relations, focusing on issues such as natural gas and the rising number of Russian tourists coming to Turkey.

Erdogan said the proposal to buy Patriots in lieu of S-400s was an "affront" to Turkey's sovereign rights. "We absolutely do not think this is right," he said.

Turkey-US ties are strained over multiple issues including Syria but they are especially tense after Ankara's purchase of the S-400 system from Moscow.

Despite repeated warnings and the risk of US sanctions under the Countering America's Adversaries Through Sanctions Act, Turkey has not rowed back from the move.

The act, known as CAATSA, was passed by Congress in 2017 and mandates sanctions for any "significant" purchases of weapons from Russia.

Following talks at the White House, Erdogan and Trump held a press conference Wednesday in which the US leader said Turkey's acquisition of the S-400 "creates some very serious challenges for us, and we are talking about it constantly."

He said the two countries' foreign ministers and national security advisers would "immediately work on resolving the S-400 issue".

The system was in fact delivered to an air base in Ankara this summer. A direct consequence of the purchase was Turkey's removal from the F-35 fighter jet programme.

Washington had repeatedly said it would not sell US-made F-35 warplanes to countries which operate the S-400 over concerns information about the extent of the stealth capabilities of the fighters getting back to Moscow.

Turkey had planned to purchase over 100 of the advanced fighters.