State Department spokeswoman Heather Nauert told reporters on Tuesday that the United States does not deem it “necessary” to appoint a new envoy to help resolve tensions between Iraq and the Kurdistan Regional Government (KRG).

The KRG is a previously fully autonomous part of Iraq that Baghdad invaded after it held an independence referendum in September. The KRG has lost control of the disputed city of Kirkuk, with Iran-backed Shiite militias threatening its borders. Its foreign minister insisted that Iraq has a “need for greater U.S. involvement” this week after meeting with some American officials.

Asked for a response to Foreign Minister Falah Mustafa, Nauert said that the United States had faith in Iraq and Kurdistan resolving their dispute “internally” and that America did not “feel that it’s necessary to appoint some sort of United States envoy in some sort of new position to handle this.”

“We will continue to try to facilitate conversations but we just don’t feel that an envoy is necessary to have—to appoint,” she added, before insisting that the Kurds had not made a “formal” request for such aid and that U.S. had already sent its special envoy for the coalition against the Islamic State, Brett McGurk, to speak to both Iraqi and Kurdish officials. Secretary of State Rex Tillerson, she added, had also reached out to Kurdish and Iraqi leadership.

McGurk met with Kurdish National Security Council head Masrour Barzani last week and pledged “his country’s support for Erbil as a constitutional entity within Iraq,” the Kurdish outlet Rudaw reported. McGurk also met Iraqi Prime Minister Haider al-Abadi. It was the first visit by McGurk since the referendum.

“So, I mean, that’s a very high level of support that we have trying to help facilitate things—for things to improve in Iraq. I don’t know that there’s that much more that we can do,” she added.

According to the Kurdish government, Foreign Minister Mustafa “stressed the need for greater U.S. involvement to ensure that ceasefire [with Iraq] is enforced and disputes are resolved through dialogue” after a meeting with American officials last week.

In an official statement on Monday, the KRG issued a call to the entire international community to “intervene with the Government of Iraq to end its collective measures against the people and government of the Kurdistan Region.” It listed among the punitive measures Baghdad had taken against the KRG “reducing the Kurdistan Region’s budget in the 2018 Draft Budget Bill without involving the Kurdistan Regional Government, closure of the Kurdistan Region’s airspace, and travel restrictions.”

Following the September referendum, in which over 90 percent of those living in the Kurdistan region voted “yes” to seceding from Iraq, Baghdad shut down the KRG’s two airports in Erbil and Sulaymaniyah. The United States did not recognize the referendum, nor did any Mideast state except Israel.

In its statement Monday, the KRG noted that not having access to air travel significant hurts efforts to help Christian, Yazidi, and other minority victims of the Islamic State (ISIS), particularly those who need to fly out of the region to receive urgent medical care. The KRG’s Peshmerga fighters are among the most loyal American allies on the ground fighting the Islamic State.

Mustafa, the foreign minister, met with U.S. National Security Adviser H.R. McMaster on Tuesday, according to the Kurdish government. “Gen. McMaster reiterated the US support for a strong and united KRG in a federal and democratic Iraq, on the basis of the Iraqi Constitution. He said that the US recognizes the role that KRG plays for regional stability,” the KRG said.

Mustafa also warned this week that a commitment to “democracy” without a sophisticated approach to protecting minorities in Iraq is “not enough.” You must build bridges between people, democracy itself is not enough,” he asserted. Iraq has suffered through a high number of attempts at genocides against Kurds, Yazidis, Christians, and other minorities. Many in Iraq distrust the Shiite-dominated Baghdad government for its ties to Iran and lack of diversity in leadership.

Baghdad made the particularly disturbing move to minorities of legalizing the Popular Mobilization Forces (PMF)—a coalition of mostly Shiite militias, many with ties to Iran—prior to the liberation of Mosul from the Islamic State. Baghdad forbade the Peshmerga from entering into Mosul city limits, sending the PMF inside, instead.

With the Islamic State defeated, the PMF had turned towards attacking Kurds and threatening American troops in Iraq.

“The U.S. has become our direct enemy after the Congress’ decision against some Hashd al-Shaabi [PMF] factions,” Abdullatif al-Amidi, a commander from the Saraya al-Ashura PMF militia, said in a speech Tuesday. Congress has issued warnings that the PMF are anti-American and have close ties to Iran. Reports following Iraq’s invasion of Kirkuk, formerly under Kurdish control, indicated that Iran had dispatched Islamic Revolutionary Guard Corps (IRGC) Quds Force head Qasem Soleimani to help the PMF in Kirkuk.

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