The Syrian opposition, meanwhile, was plunged into crisis as its leader quit after expressing frustration with a lack of support for the rebels from the international community.
The 2-year-old war in Syria spilled over the border Sunday as Israeli troops in the Golan Heights destroyed a Syrian military machine gun position after coming under fire from that area. Israeli Defense Minister Moshe Yaalon blamed the Syrian military for the incident.
Iran’s Shiite regime has provided a steady stream of military support to Mr. Assad even as the international community has debated the wisdom of arming the Syrian opposition.
More than 70,000 people have been killed in the uprising against the Assad regime and more than 1.1 million refugees have fled to Syria’s neighbors, the U.N. says.
The Obama administration, alarmed by the support Mr. Assad receives from Tehran, wants the Iranian flights through Iraqi airspace to stop or, at the very least, be inspected in Iraq to ensure that they are carrying humanitarian supplies.
Iraqi Prime Minister Nouri al-Maliki’s government last year promised then-Secretary of State Hillary Rodham Clinton that it would inspect the Iranian planes.
Only two planes have been inspected since July, said a senior U.S. official who spoke on background. In both cases, Iraqi inspectors found humanitarian supplies.
Mr. Kerry said Iranian support has sustained the Assad regime and that he had a “very spirited discussion” with Mr. al-Maliki on this subject when they met in Baghdad.
Urging Mr. al-Maliki to put an end to such support, Mr. Kerry said some members of Congress and the American people are “wondering how it is that a partner for whom Americans feel they have tried so hard to be helpful … can be, in fact, doing something that makes it more difficult to achieve our common goals.”
The Iranian flights to Syria occur “close to daily,” said the senior U.S. official who spoke on background. “It goes up and down. But it’s substantial.”
The official, who spoke before Mr. Kerry’s meeting with Mr. al-Maliki, said the secretary of state would “be very direct with Prime Minister Maliki about the importance of stopping the Iranian overflights and the transits across the territory, or at minimum inspecting each of the flights.”
“And his goal is not to get into a tit-for-tat about how we know this or how we know that, but to explain that the number of the flights is, in itself, an indication that these can’t possibly be only humanitarian flights and that he, himself, as secretary of state, is convinced that they include weapons and fighters and that this is absolutely contrary to the international goals with Syria and is dangerous for Iraq,” the official added.
On Sunday, the Western-backed Syrian opposition coalition was dealt a blow when its leader, Moaz al-Khatib, resigned saying the international community has not done enough to support to the rebels.
“I promised the Syrian people and God to resign if matters reach some red lines,” Mr. al-Khatib said in a statement announcing his resignation as head of the Syrian National Coalition. Mr. al-Khatib was chosen to serve as president of the coalition when it was formed in November.