"We have made it absolutely clear... That they must go back across the river," Biden said at a news conference with Turkish Prime Minister Binali Yildirim.
"They cannot, will not and under no circumstances (will) get American support if they do not keep that commitment. Period."
His comments come after Turkish troops today launched an operation inside Syria to cleanse the key town of Jarabulus from Islamic State (IS) jihadists.
Turkey fears that Syrian Kurds may have designs on Jarabulus after seizing the strategic Manbij area in northern Syria from IS.
Ankara has said any attempt by the YPG -- the Syrian Kurdish People's Protection Units -- to move west of the Euphrates would be crossing a red line. YPG fighters are already well installed in northeastern Syria.
Speaking alongside the US vice president, Yildirim confirmed an agreement with Washington that "PYD elements will not move to the west of the Euphrates and will not be engaged in any activity there."
"PYD/YPG elements can never exist west of Euphrates under any circumstances, we have confirmed once more (US) sensitivity on this issue.
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