Mr Kerry, on an unannounced trip to Iraq, held talks with Prime Minister Nouri Maliki in a bid to boost co-operation over the Syria conflict.
He said Iranian arms were sustaining Syrian President Bashar al-Assad.
The US has accused Iraq of turning a blind eye to the flights, which Iran claims transport only humanitarian aid.
It is 10 years since the US-led invasion of Iraq that toppled former Iraqi President Saddam Hussein.
The trip is Mr Kerry’s first to Iraq since taking office earlier this year, and the first by an American secretary of state since 2009.
“I made very clear to the prime minister that the overflights from Iran are in fact helping to sustain President Assad and his regime,” Mr Kerry told reporters.
“I made it very clear that for those of us who are engaged in an effort to see President Assad step down… anything that supports President Assad is problematic.”
An unnamed US official earlier told the AP news agency that Iranian planes were flying over Iraq into Syria almost every day.
The official said Iraq had promised to inspect the flights, but only two planes had been checked since last year.
The state department said Mr Kerry would also discuss democratic reforms in Iraq.
He was expected to suggest that Iraq’s government reconsider a recent decision to delay provincial elections in Anbar and Nineveh provinces.
And he was also expected speak by phone to Massoud Barzani, president of the oil-rich autonomous region of Kurdistan, to stress the importance of maintaining Iraq’s unity.