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5 year oldMr Pompeo defended President Donald Trump's decision to withdraw US troops from the border area, which has sparked an outcry at home and abroad.
Turkey has now launched an assault on territory held by Kurdish-led forces.
President Recep Tayyip Erdogan said the aim was to "prevent the creation of a terror corridor" on the border.
Turkish forces plan to make a "safe zone" cleared of Kurdish militias which will also house Syrian refugees.
Kurdish-led forces vowed to resist the offensive and have already clashed with Turkish troops.
The Kurds - who helped defeat the Islamic State (IS) group in Syria and were key US allies in that fight - guard thousands of IS fighters and their relatives in prisons and camps in areas under their control. It is unclear whether they will continue to do so if battles break out.
The US military says it has taken custody of two British detainees notorious for their roles in an IS cell that tortured and killed nearly 30 Western hostages.
The two men, El Shafee Elsheikh and Alexanda Kotey, were part of a British cell nicknamed The Beatles.
They have now been removed from a prison run by the Kurdish-led militia in northern Syria.
In an interview with US broadcaster PBS, Mr Pompeo defended Mr Trump's surprise decision to pull back US forces, adding that Turkey has a "legitimate security concern" and "a terrorist threat to their south".
He said reports the US had allowed Turkey to launch the offensive were "just false".
"The United States didn't give Turkey a green light," he said.
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