Pentagon officials on Monday said U.S. military commanders in Iraq are urging Iraqi and Kurdish forces to “avoid additional escalatory actions” following a skirmish over the capture of the Kurdish-held city of Kirkuk.

“We strongly believe that dialogue still remains the best option to the ongoing tensions,” Defense Department spokesman Col. Robert Manning told reporters at the Pentagon.

“Commanders on the ground are engaged,” he said.

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Early Monday, Iraqi forces advanced into the disputed province of Kirkuk, which the Kurds have controlled since ousting the Islamic State in Iraq and Syria (ISIS) in 2014. By midday, Iraqi forces had seized oil fields north of the city, its airport and a military base, The Associated Press reported.

The Iraqi government forces were responding to a Kurdish vote on independence, which was non-binding but raised tensions over the oil-rich Kirkuk province.

The two sides also exchanged fire Monday, which the U.S.-led military coalition in Iraq downplayed as a “misunderstanding.”

Pentagon spokesman Major Adrian Rankine-Galloway said U.S. coalition forces were “in the vicinity” of Kirkuk at the time of the incident.

“We do not consider them to be threatened or in any kind of danger and there are appropriate force protection measures in place to ensure their safety,” Rankine-Galloway said of the U.S. special forces.

About 5,200 U.S. troops are in Iraq, and the U.S. military has trained and armed both Iraqi and Kurdish forces in the fight against ISIS.

Manning would not say if or when the U.S. might cut off military aid and training to Iraqi forces should a major conflict begin.

“I’m not going to speculate on that. We’re looking at all options for planning considerations and we’d have to address that down the road,” Manning said.

“Right now it is a distraction to do anything but focus on killing ISIS. And so what we’re doing right now is making sure that both sides understand that this is not helpful, and although we support a unified Iraq, we do not support both sides going after each other,” Manning said.

Lawmakers spoke out against the conflict on Monday, including Senate Minority Leader Charles Schumer (D-N.Y.), who urged the White House to start a dialogue between the two sides.

“Every ounce of energy and resources the Iraqi government and the Kurdish Peshmerga spend fighting each other should instead be spent fighting ISIS and terrorism in the region,” Schumer said in a statement.

“This is especially true when those resources are those sent by the United States. I urge the administration to immediately initiate a dialogue between the two sides to ensure a peaceful resolution between the Iraqi government and Iraqi Kurds that doesn’t jeopardize the ongoing fight against ISIS," the statement continued.

And Sen. John McCain (R-Ariz.) on Monday warned Baghdad of “severe consequences” if it uses U.S. arms against the Kurds.