The White House’s top envoy in the fight against the Islamic State made clear Thursday that Washington and its allies will not support Kurdish plans to hold an independence referendum vote in northern Iraq.

The vote and subsequent bid for an independent Kurdish state would be “significantly destabilizing” in the wake of Baghdad’s recent liberation of Mosul from the terror group known as ISIS or ISIL. Baghdad’s successful recapture of Iraqi’s second-largest city is one of the most significant victories against ISIS since the U.S.-backed offensive against the group began in earnest two years ago.

But that victory could be fleeting, if Erbil’s push for independence causes the fragile Iraqi coalition of ethnic rivals cobbled together by Washington to fall apart, Special Presidential Envoy for the Global Coalition to Defeat ISIS Brett McGurk said Thursday.

The timing of the vote and the speed in which officials from the Kurdistan Regional Government are pushing to hold the vote could put Baghdad in a politically dangerous position, as the central government attempts to find common ground within the country’s sectarian conflicts for a post-ISIS Iraq.

“We think that under the Iraqi constitution, there’s an important process of dialogue that has to take place, and having a referendum on such a fast timeline, particularly in disputed areas, would be, we think, significantly destabilizing,” Mr. McGurk told reporters after a anti-ISIS coalition meeting at the State Department on Thursday.

An Iraqi delegation from Bagdad recently traveled to Erbil, to discuss the internal and regional ramifications of a Kurdish independence bid, Mr. McGurk said. “That’s the type of dialogue I think we need to see,” he said. Mr. McGurk is the second senior national security official to publicly oppose the referendum vote, slated for September.