The visit, his first to Baghdad since taking office, will also focus on concerns in Washington that months of protests in the country's Sunni-majority provinces will give militant groups including Al-Qaeda room to manoeuvre.
It comes just days after the 10th anniversary of the US-led invasion of Iraq that ousted Saddam Hussein and sought to establish a stable democratic ally in the heart of the Middle East, but has instead left a country still grappling with deadly violence and endless political disputes.
Kerry will meet Prime Minister Nuri al-Maliki and parliament speaker Osama al-Nujaifi and press Iraqi officials for greater cooperation on isolating the regime of embattled Syrian President Bashar al-Assad.
Washington has accused Baghdad in particular of turning a blind eye as Iran sends military equipment through Iraqi airspace, flights which Tehran insists transport only humanitarian supplies.
Kerry "will be very direct with Prime Minister Maliki about the importance of stopping the Iranian overflights and the transit across the territory, or at minimum inspecting each of the flights," a State Department official said, speaking on condition of anonymity.
"He himself, as secretary of state, is convinced that they include weapons and fighters. ... This is dangerous for Iraq."
Baghdad has announced the inspections of two such flights, both in October 2012, but the New York Times reported in December that Iran appears to have been tipped off by Iraqi officials as to when plane inspections would be conducted, thus helping Tehran avoid detection.
A US official this month called on Iraq to resume unannounced inspections of Iranian flights bound for Syria.
"They are suspending their disbelief, looking the other way, and averting their gaze," the official said.
Iran has remained a steadfast ally of Assad's regime despite the conflict in his country which according to the United Nations has killed more than 70,000 people since it erupted in March 2011.
The top US diplomat will also push for Iraq's Shiite-led government to better engage with its Sunni Arab minority, which has been protesting since December over the alleged targeting of their community by the authorities.
In particular, Kerry will push for Maliki to reconsider a decision to postpone upcoming provincial elections, scheduled for April 20, in two large Sunni-majority provinces.
He will also call on Nujaifi, a senior leader in the Sunni-backed Iraqiya movement that is part of Maliki's unity cabinet but has boycotted government meetings, to push for ministers to return to the table.
"Secretary Kerry will be talking with Prime Minister Maliki about the importance of engaging with all elements of Iraqi society, with the Sunnis, to work out how best to counter the very serious terrorist threat that is (of) deep concern to Iraqis," the official said.
Kerry will also "suggest to Nujaifi that he returns his colleagues to the cabinet" and "that it is far preferable for him to engage no matter what he thinks about Maliki."
A Western diplomat warned last week that Washington was concerned by "the vacuum that it (protests in Sunni provinces) creates for Al-Qaeda to come in and play a role."
Kerry's visit comes amid claims of declining American influence in Iraq, in particular following the December 2011 withdrawal of US forces, and concerns that Baghdad's Shiite neighbour Iran wields greater clout.
The American mission to Iraq, however, remains the biggest in the world and US officials have consistently disputed arguments that Washington's influence is waning.
"It is not re-engagement, but it is to demonstrate our commitment to intensive engagement with Prime Minister Maliki and various players in Iraq," the State Department official said. "He does not have to rely only on Iran for support."