Secretary of State John Kerry met Tuesday with Kurdish leader Massoud Barzani in a bid to convince him to close ranks with the government in Baghdad to fend off an insurgency by Sunni militants.
It was the secretary's final round of diplomacy with Iraqi leaders before leaving the country.
Kerry's visit to Iraqi Kurdistan came amid a new round of conflicting reports that Islamic State of Iraq and the Levant [ISIL] militants had captured Iraq's largest oil refinery at Beiji, north of Tikrit.
VOA could not independently confirm who is in control of Beiji.
Amateur video showed the aftermath of a bombing raid over the militant-controlled Iraqi border town of Qaim, facing Syria. Witnesses claim Syrian warplanes bombed militant positions from the air.
Beiji oil refinery, Iraq
In Kurdistan, Kerry thanked the Kurdish leader for helping battle the militants during their meeting. He went on to stress that resolving the current conflict revolves around forming an inclusive new government in Baghdad.
“As everybody knows, this is a very critical time for Iraq as a whole and the government formation challenge is the central challenge that we face," Kerry said. "In recent days the security cooperation between the forces here in the Kurdish area has been really critical in helping to draw a line with respect to ISIL and also to provide some support to the Iraqi security forces.”
But Barzani was cautious about cooperating with the Baghdad forces, saying it was impossible to fight the militants, "without a clear future, a complete agreement and a complete political solution."
Kerry told U.S. broadcaster CBS that President Barack Obama is not planning to help the government of Prime Minister Nouri al Maliki with air support, due to the lack of political consensus among Iraqi leaders. He said it would be a "total act of irresponsibility" for the president to order air strikes when the current Iraqi government is not unified.
US military's assessment
The first of the 300 military advisers U.S. President Barack Obama has committed to help Iraq counter a Sunni militant surge have begun their assessment mission.
Pentagon spokesman Rear Admiral John Kirby said two special operations teams -- a total of 40 personnel already working in Iraq -- started their work on Tuesday.
He said an additional 90 troops, flown in by the U.S. Central Command, are now in the Iraqi capital to set up a new Baghdad joint operations center.
Another four teams will arrive within the next few days, bringing the total number of U.S. personnel to nearly 200.
The United States also is conducting air surveillance over Iraq, with 30 to 35 flights a day to help gain better insight about the security situation on the ground as Iraqi troops battle the fast-moving insurgency.
The advance of the Sunni militants, ISIL, has sparked a crisis in Iraq.
Secretary Kerry sits with Iraqi Prime Minister al-Maliki before meeting in Baghdad, June 22-27, 2014.
On Monday, Kerry met with al-Maliki, a key Shi'ite cleric and the two highest-ranking Sunni lawmakers.
He said Monday Iraqi leaders assured him they would meet a July 1 deadline to start forming a new government, but he warned the Iraqis they must act quickly to block the advance of the militants.
The prime minister's office said al-Maliki told Kerry that the insurgents' advance "represents a threat not only to Iraq but to regional and international peace." The Iraqi leader called for U.S. air strikes against the insurgents, which the U.S. is considering.
The U.S. has not publicly called for Maliki to leave office, but has repeatedly pushed him to create a government that includes more authority for Sunnis and Kurds.
After his stop in Iraq, Kerry is due to travel to Brussels for a meeting of NATO foreign ministers, and State Department officials say they expect to have discussions there with European partners about the situation in Iraq.
Click here to read Secretary Kerry's comments in Baghdad, June 23, 2014.
Edward Yeranian contributed to this report from Cairo.