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 the BBC 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.
President Trump has faced intense criticism for the withdrawal of troops, which some say effectively gave Turkey the green light to launch the military attack.
Much of the criticism has come from within Mr Trump's own party.
In a rare bipartisan rebuke, 129 members of the president's Republican Party in the House of Representatives joined Democrats to formally denounce the move in a vote on Wednesday.
House Speaker Nancy Pelosi also held an apparently explosive meeting with President Trump on the issue, which led to her and Senate Minority Leader Charles Schumer walking out of the room.
Ms Pelosi and Mr Trump both later accused each other of having a "meltdown".
Republican leaders said Ms Pelosi's behaviour was "unbecoming", and criticised her for "storming out".
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".
Turkish troops and allied Syrian rebels launched the offensive in northern Syria last week to push back from the border members of a Syrian Kurdish militia, called the People's Protection URead More – Source