The incident, which has not been confirmed by Washington, is expected to strain already tense relations between the two countries over the presence of Turkish soldiers in northern Iraq.
A government source said 11 or more Turkish soldiers stationed in northern Iraq had been held by US forces on Friday afternoon.
"They are talking about an event with the municipality in Kirkuk. There is nothing about this that could be approved of or looked upon positively. It's a totally ugly incident, it's something that shouldn't have happened," Erdogan said.
Hurriyet newspaper said the Turkish soldiers were accused of planning an attack on a regional Kurdish governor. Government sources were unable to confirm this.
The paper said around 100 US troops on Friday moved on barracks used by Turkish soldiers in Sulaymaniyah and transferred the Turkish officers to the city of Kirkuk.
"We cannot understand the Americans' aims," deputy armed forces chief Yasar Buyukanit was quoted as saying. "This action by our ally of 50 years has deeply saddened and shaken us."
Relations between Washington and Ankara soured before the US war on Iraq when Turkey's parliament refused to allow US forces to stage attacks on its neighbour from Turkish soil.
A few thousand Turkish troops remain inside northern Iraq in pursuit of Turkish Kurdish guerrillas who waged a separatist campaign in the 1980s and 1990s in southeastern Turkey.
Turkey has long expressed fears Kurds in northern Iraq might try to create an independent state.
Ankara fears this could reignite a separatist rebellion in its largely Kurdish southeast.
US-backed Kurdish leaders who have run northern Iraq since the end of the 1991 Gulf war have urged Turkey to withdraw its troops from the enclave to stabilise the region.