Turkish President Recep Tayyip Erdogan put US President Donald Trump's letter "in the bin", the BBC has been told.
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 BBC Turkish 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 favourably 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."
It is hard to imagine language like it in many letters between presidents.
Donald Trump's mixture of threats and locker-room banter infuriated Turkey's President Recep Tayyip Erdogan. His staff told the BBC that he threw the letter into the bin and launched the Syrian operation the same day. That could be proof there was no Trumpian green light.
But ever since President Obama partnered up with the Syrian Kurds of the Syrian Democratic Forces (SDF) against the jihadists of IS it was clear the arrangement would lead to problems with the Turks. That's because the SDF is very close to the Turkish Kurds of the PKK. Turkey says they are two halves of the same terror group.
Presidents Erdogan and Trump discussed military action last December. Diplomatic sources here in Ankara suggest that Turkey's broader strategic objective was to detach the Kurds and the Americans.
That, at any rate, has happened.
The diplomatic debacle that has surrounded events in and around Syria is the background to President Erdogan's meeting in Ankara with a US delegation headed by Vice-President Mike Pence, with Secretary of State Mike Pompeo. It is hard to find common ground between the two sides.