Sen. John McCain on Monday called on Iraq to halt its advance on separatists in the north amid flaring tensions and clashes as government forces reclaim territory from Kurds forces in the northern part of that country.

Iraqi Prime Minister Haider al-Abadi and the Kurdish regional government should begin a dialogue on halting hostilities and about greater autonomy for the Kurds, who recently voted overwhelmingly to break away from Baghdad and form an independent state, McCain said.

The Arizona Republican and Senate Armed Services chairman also warned of "severe consequences" if the competing factions destroy military equipment supplied by the United States. Reports on Monday claimed Kurdish Peshmerga forces destroyed at least five U.S. Humvees that were used by Iran-backed Shiite militias.

"The United States provided equipment and training to the Government of Iraq to fight ISIS and secure itself from external threats — not to attack elements of one of its own regional governments, which is a longstanding and valuable partner of the United States," McCain said in a statement. "Make no mistake, there will be severe consequences if we continue to see American equipment misused in this way."

Iraqi forces have begun moving into Kirkuk to reclaim the city and the area's oil fields, which were wrested from the Islamic State group by the Kurdish Peshmerga in 2014 and held by them since.

The central government and the ethnic Kurds have a long fraught relationship, including oppression and a deadly chemical weapons attack by former Iraqi dictator Saddam Hussein. But a Kurdish vote last month where 93 percent of the region's 3.9 million residents voted for independence has suddenly ratcheted up those long-simmering tensions.

Meanwhile, the U.S. is caught in the middle as it works with both the Iraqi Security Forces and the Kurdish Peshmerga to defeat the Islamic State in its last holdouts in the country.