WASHINGTON (REUTERS) - United States President Donald Trump warned Turkish President Recep Tayyip Erdogan in a letter about Turkey's incursion into Syria: "Don't be a tough guy" and "Don't be a fool!"

The Oct 9 letter was released by the White House on Wednesday (Oct 16) as Mr Trump battled to control the political damage following his decision to pull US troops out of northern Syria, clearing the way for the Turkish incursion against America's Kurdish allies.

The letter tried to persuade Mr Erdogan to reverse a decision to invade Syria that the Turkish President told Mr Trump about in an Oct 6 phone call.

"Let's work out a good deal!" Mr Trump said. "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."

The US President had the letter released to bolster his view that he did not give Turkey a green light to invade Syria. Many lawmakers have been sharply critical of his decision to remove American forces from the conflict zone.

"I have worked hard to solve some of your problems. Don't let the world down. You can make a great deal," said Mr Trump in the letter.

He wrote that the commander of the Kurdish-led Syrian Democratic Forces, General Mazloum Kobani Abdi, was willing to negotiate and to make some concessions.

He said he had confidentially enclosed to Mr Erdogan a copy of a letter Gen Mazloum had sent him.

"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. Don't be a tough guy. Don't be a fool!" said Mr Trump.

He added: "I will call you later."