Turkey has so far rebuffed international pressure to hold its fire against Kurdish forces in the war-torn Middle Eastern nation.
"Additional sanctions will be coming if they don't institute a ceasefire," Mnuchin told reporters.
US Vice President Mike Pence was due to travel on Wednesday to Ankara, where he is likewise expected to demand a ceasefire.
But earlier on in the day, Turkish President Recep Tayyip Erdogan had already dismissed US calls for a ceasefire, according to local media reports.
Erdogan also said Ankara was "not worried" about previously announced US sanctions.
Turkey last week began an operation to drive back Syrian Kurdish militants from northern Syria, after the US pulled 1,000 troops out of the area.
The withdrawal was seen as a green light from the White House for the Turkish offensive, creating a massive backlash for Trump.
The American president meanwhile has sent mixed messages, at times threatening Ankara, and at others, suggesting the US had no role in the fight between Turkey and Kurdish militants.
Clashes have continued across the region, with Kurdish fighters in the border town of Ras al-Ain burning tires in a bid to blind Ankara's warplanes and digging in against a ground offensive by Turkish-backed Syrian rebels.
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