He was speaking in the United Arab Emirates following a phone call with his Turkish counterpart.
US forces in northern Syria have fought alongside a Kurdish militia against Islamic State (IS) militants.
Turkey, however, regards the People’s Protection Units (YPG) as a terrorist group and has vowed to crush it.
Mr Pompeo is touring the Middle East to try to reassure allies following President Donald Trump’s abrupt announcement last month that US forces would withdraw from Syria.
Talking to reporters in Abu Dhabi, Mr Pompeo said the US recognised “the Turkish people’s right and [Turkish President Recep Tayyip] Erdogan’s right to defend their country from terrorists”.
“We also know that those fighting alongside us for all this time deserve to be protected as well,” he said.
Mr Pompeo said he had spoken to Turkish Foreign Minister Mevlut Cavusoglu, adding: “Many details (are)…