Turkish President Recep Tayyip Erdogan put US President Donald Trump's letter "in the bin",
In the letter dated 9 October, and sent after US troops were pulled out of Syria, Mr Trump told Mr Erdogan: "Don't be a tough guy. Don't be a fool!"
Turkish presidential sources told to International News Outlet that the letter was "thoroughly rejected" by Mr Erdogan.
On the day the letter was received, Turkey launched a cross-border offensive against Kurdish-led forces.
"Let's work out a good deal! You don't want to be responsible for slaughtering thousands of people, and I don't want to be responsible for destroying the Turkish economy - and I will," Mr Trump said in the letter.
"History will look upon you favorably if you get this done the right and humane way. It will look upon you forever as the devil if good things don't happen."
In response, Turkish presidential sources said: "President Erdogan received the letter, thoroughly rejected it and put it in the bin.
Earlier on Wednesday, President Trump said the US should not be intervening in Turkey's military operation in Syria because it is "not our border", and called the former US allies the Kurds "no angels".
"They have a problem at a border," he told reporters at the White House. "It's not our border. We shouldn't be losing lives over it."
The president also said he thought the situation on the Turkey-Syria border was "strategically brilliant" for the US.
"Our soldiers are out of there. Our soldiers are totally safe. They've got to work it out. Maybe they can do it without fighting," he said.
"We're watching and we're negotiating and we're trying to get Turkey to do the right thing, because we'd like to stop wars regardless."
On the Kurds, he added: "They fought with us. We made a lot of money for them to fight with us, and that's okay. They did well when they fought with us. They didn't do so well when they didn't fight with us."