The move came after the US agreed to withdraw its troops from the area, leaving the Syrian Democratic Forces (SDF), its main ally in the battle against the Islamic State of Iraq and the Levant (ISIL or ISIS) armed group, without US military support.
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The Syria offensive had already set off a mass displacement of civilians and sparked fears it could lead to a resurgence of the Islamic State militant group.
Pence and Erdogan met at the presidential palace in Ankara, making little effort to hide the tensions between their two governments: They shook hands but neither Pence nor Erdogan smiled while posing for photographs.
Pence's mission came a day after the White House made public a letter Trump had sent to Erdogan on October 9 urging the Turkish leader to make a deal with the Syrian Kurdish militias that are the target of Ankara's military operation.
"You don't want to be responsible for slaughtering people," Trump wrote, concluding: "Don't be a tough guy. Don't be a fool!" The letter was written on the day Turkey's military operation started.
Turkish officials told the BBC and other news outlets Thursday that Erdogan threw the letter in the trash.
Erdogan has rebuffed appeals for a cease-fire and chided Western allies for suggesting he negotiate with "terrorists," as he refers to the Syrian Kurdish militias because of their links with the Kurdistan Workers' Party, or PKK, which has fought an insurgency in Turkey for decades.
Erdogan said Wednesday that Turkey would "never declare a cease-fire" and vowed to forge ahead with plans to enforce a buffer zone as deep as 20 miles into Syrian territory. The swath of territory would stretch more than 280 miles from the northern city of Manbij to the Syrian border with Iraq.
Turkey's offensive, which includes its own bands of Syrian rebels, has upended alliances and reignited tensions in a particularly volatile corner of Syria, where U.S. troops for years partnered with Kurdish-led fighters to battle the Islamic State.