US Vice President Joe Biden says the Syrian Kurdish forces his country backs must go back across the Euphrates River to the east bank.
"They cannot, will not, and under no circumstances get American support if they do not keep their commitment," Biden says.
He also says the US will not accept a Kurdish entity on the Turkish border.
The US is providing air cover and advisors for the Turkish military operation in Jarablus in north Syria.
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Turkey has shelled positions of the US-backed, Kurdish-led Democratic Forces of Syria, in northern Syria, a senior official says.
Syrian Kurds condemn the Turkish incursion into Islamic State-held Jarablus, calling it a "declaration of war."
Turkish jets launched airstrikes against the northern Syrian town of Jarablus on Wednesday to clear it of Islamic State militants, state media reported saying it was a joint operation with the US-led coalition.
Turkish tanks crossed the border into Jarablus in northern Syria, state broadcaster TRT reported Wednesday citing military sources, while Syrian rebels forces told dpa they are also crossing into the Islamic State-held town from Turkey.