Mr Kerry flew into Baghdad on Saturday from Amman after accompanying President Barack Obama to Israel and Jordan.
Officials travelling with him said he would press Iraqi Prime Minister Nouri al-Maliki and other senior officials on democratic reforms and urge them to stop overflights of Iranian aircraft carrying military personnel and equipment to support the Syrian government as it battles rebels.
The flights have been a source of contention between the US and Iraq and Mr Kerry will tell the Iraqis that letting them continue will threaten the country’s stability.
A senior US official said the sheer number of overflights, which occur as well as overland shipments to Syria through Iraq from Iran, was inconsistent with Iranian claims that they are only carrying humanitarian supplies.
The official said it was in Iraq’s interest to prevent the situation in Syria deteriorating further, particularly as there are fears that Iranian-backed extremists may gain a foothold there.