BAGHDAD -- Secretary of State John Kerry told Prime Minister Nuri Kamal al-Maliki during a visit to Baghdad on Sunday that Iraq must take steps to stop the shipment of Iranian weapons to Syria if it wanted to participate in broader discussions about that country's future.
Mr. Kerry's visit was the first by an American secretary of state since Hillary Rodham Clinton went to Iraq in 2009, and it came amid growing concern over Iraq's role in the Syrian conflict.
Flights of Iranian weapons to Syria through Iraqi airspace, which a senior State Department official said were occurring on nearly a daily basis, have been crucial for the government of President Bashar al-Assad of Syria, which faces increasing pressure from rebel fighters. Mr. Kerry said he had a spirited discussion with Mr. Maliki about the issue, but there was no tangible sign that the Iraqis would alter their position.
Mr. Kerry, speaking at a news conference at the American Embassy here after meeting with the prime minister, said he stressed that supporting Mr. Assad by allowing the flights is "problematic" and did not represent the "common goals" of the United States and Iraq.
The air corridor over Iraq has emerged as a main route of military aid to Mr. Assad's government. The shipments include rockets, antitank missiles, rocket-propelled grenades and mortars, and Iranian personnel, according to American intelligence officials. There are supply lines on the ground as well.
Iran has as an enormous stake in Syria, which is its staunchest Arab ally and has provided a channel for Iran's support to the Islamist movement Hezbollah in Lebanon.
Syria is also important to the Shiite-dominated Iraqi government, led by Mr. Maliki. Fearing that Mr. Assad's overthrow would lead to Sunni control and embolden the Iraqi Sunnis who oppose him, Mr. Maliki has been seen as tolerating the Iranian flights.
American officials have repeatedly insisted that the Iraqis demand that the Iranian flights must land so that they can be inspected. But the Iraqis have only carried out two inspections since July, the State Department official said. One was of an Iranian flight that was on its way back to Tehran after delivering its cargo in Syria. Iran has said the flights are merely carrying humanitarian aid.
Iraq has yet to develop an air force, and since the United States military left the country in 2011, American warplanes no longer patrol Iraq's skies.
The Iranian flights pose a major challenge for American strategy on Syria. Mr. Kerry has repeatedly said that Obama administration officials want to change Mr. Assad's calculation that he can prevail militarily, and they want to persuade him to relinquish power and agree to a political transition. But Robert Ford, the senior State Department official on Syria policy, told Congress last week that Iranian and Russian military assistance has fortified Mr. Assad's belief that his military can still win.
As a senator, Mr. Kerry suggested that the United States should consider linking its support for Iraq with Mr. Maliki's willingness to order the inspection of the Iranian flights. "If so many people have entreated the government to stop and that doesn't seem to be having an impact," Mr. Kerry said in September when he was chairman of the Senate Foreign Relations Committee, "that sort of alarms me a little bit and seems to send a signal to me maybe we should make some of our assistance or some of our support contingent on some kind of appropriate response."
As secretary of state, Mr. Kerry has adopted a less confrontational approach.
Concerning Iraq's fraught political scene, Mr. Kerry pushed Mr. Maliki to reconsider a recent decision to postpone provincial elections in Anbar and Nineveh Provinces, where protests are continuing by Sunnis -- which dominate the two provinces but which are a minority in Iraq as a whole. The Iraqi government has justified the delay by citing security concerns.
"Everyone needs to vote simultaneously," he said on Sunday, adding that "no country knows more about voting under difficult circumstances than Iraq." The elections had been scheduled for April 20.
Mr. Kerry also met with Osama al-Nujaifi, a Sunni who is the speaker of the Iraqi Parliament, and spoke by telephone with Massoud Barzani, the leader of the Kurdish Regional Government, who is in Erbil.
A leading Sunni, Rafi al-Essawi, recently resigned his post as finance minister to protest Mr. Maliki's reluctance to share power with Sunni leaders. A warrant has been issued for Mr. Essawi's arrest -- on accusations that he has links to terrorists, which senior American officials have denied -- and he has reportedly sought refuge with Sunni tribes in Anbar Province.
Mr. Kerry did not specifically discuss Mr. Essawi's case with Mr. Maliki, but he did have a broad conversation with the prime minister about human rights concerns, aides said.
The trip comes as American influence in the country has begun to recede. The former defense secretary Leon E. Panetta told the United States' special inspector general on Iraq reconstruction that the withdrawal of American forces in 2011 had limited Washington's influence over Mr. Maliki, according to a report issued this month by the inspector general.
Ryan Crocker, the former American ambassador in Baghdad, has urged the Obama administration to step up its engagement with Iraqi leaders. "What it is time for," Mr. Crocker told a conference at the Carnegie Endowment on International Peace last week, is "sustained engagement."
Aides to Mr. Kerry said that was one purpose of his trip.
This article originally appeared in The New York Times.