"We have applied economic sanctions in many places, I assume he is speaking about those kinds of things, Pompeo said, adding he had not spoken with Ankara since Trump's comment.
Trump said on Sunday the US was starting the military pull-out from Syria that he announced in December but that it would continue to hit Islamic State fighters there.
"Will attack again from existing nearby base if it reforms. Will devastate Turkey economically if they hit Kurds. Create 20 mile safe zone...Likewise, do not want the Kurds to provoke Turkey," Trump wrote on Twitter.
Ankara is well aware of the cost of strained ties with the US. A diplomatic crisis last year, when Trump imposed sanctions on two of President Tayyip Erdogan's ministers and raised tariffs on Turkish metal exports, helped push the Turkish lira to a record low in August.
Turkish presidential spokesman Ibrahim Kalin said Trump should respect Washington's alliance with Ankara.
"Mr (at)realDonaldTrump It is a fatal mistake to equate Syrian Kurds with the PKK, which is on the US terrorists list, and its Syria branch PYD/YPG," spokesman Ibrahim Kalin wrote on Twitter.
"Terrorists can't be your partners & allies. Turkey expects the US to honour our strategic partnership and doesn't want it to be shadowed by terrorist propaganda," he said on Monday.
Trump gave no details about the safe zone proposal, but Pompeo said Washington wanted to provide security for those who have fought against IS and to prevent any attack on Turkey from Syria.
"If we can get the space and the security arrangements right it would be a good thing for everyone in the region," Pompeo added said.
Turkish Foreign Minister Mevlut Cavusoglu said Ankara was not against the idea of a secure zone along the border, but said strategic partners and allies should not communicate over social media.
"Nothing can be achieved by threatening Turkey economically. We need to look at how we can coordinate together and how we can solve this," he said in a news conference with Luxembourg's foreign minister.
The Kurdish YPG has been a US ally in the fight against the jihadists and it controls swathes of northern Syria. Erdogan has vowed to crush it in the wake of Trump's decision to pull US troops out of the region.