About 300 Turkish soldiers, carrying only light weapons, entered an area of the mountainous northern Kurdish province of Dahuk, about 200 km from the Iraqi city of Kirkuk, where Rice's plane first touched down.
The soldiers clashed with Kurdish separatist guerrillas, a Turkish military official said. Turkey said it has the right to use military force to combat Kurdish rebels who shelter in the semi-autonomous Kurdish region of northern Iraq.
The incursion was a sharp reminder that while violence in Iraq has dropped by 60 per cent since June, security is fragile and Iraq still faces threats. The Kurdish Regional Government condemned the incursion.
Making her eighth visit as secretary of state, Rice was expected to pressure Prime Minister Nuri al-Maliki's Shi'ite-led government to break a political deadlock and reach an accommodation with minority Sunni Arabs and Kurds.
As a helicopter carrying Rice and her entourage landed in Baghdad’s heavily protected Green Zone, which houses the US embassy complex and the Iraqi government, a car bomb exploded in central Baghdad, across the Tigris River, killing four people and wounding seven, police said.
Rice first flew into Kirkuk, a mixed city of Kurds, Arabs and Turkmen which is 250 km north of Baghdad. The city is seen as the next powderkeg in Iraq, with Kurdish nationalists demanding it be included in their largely autonomous region.
Her decision to start her visit in Kirkuk appeared part of the new US policy of focusing more on fostering reconciliation at a local and regional level. Kirkuk, with its huge oil reserves and potential for destabilising violence, is key. Iraq’s minority Kurds see Kirkuk as their historical capital, but Arabs encouraged to move there under Saddam Hussein want it to remain under the sway of the Baghdad government.