Abbott made the threat on Twitter in response to news that students at Texas State University are petitioning administrators to make the campus a "sanctuary for undocumented students, workers, and community members." Such concerns have spiked following the election of Trump, who has promised to deport millions of people in the country illegally.

"Texas will not tolerate sanctuary campuses or cities," Abbott said. "I will cut funding for any state campus if it establishes sanctuary status."

Additional details on Abbott's threat were not immediately available.

The definition of a "sanctuary campus" is not entirely clear. The University of Pennsylvania, for example, has branded itself a sanctuary campus after announcing it will not let federal immigration authorities on campus without a warrant.

At Texas State, students are asking the administration to "guarantee student privacy by refusing to release information regarding the immigration status of students, staff, and/or university community members." Similar petition efforts are currently underway at the University of Texas at Austin and University of North Texas.

At Texas A&M University, administrators met with a group of faculty this week to discuss the concept. But in an interview Thursday morning before Abbott’s tweet, university President Michael Young said he didn’t see a need for schools to make such a declaration. Federal regulations currently prevent immigration authorities from coming onto campuses except in extraordinary cases, and any changes to that policy wouldn't happen quickly, he said.

“If there is any possibility of that happening, it is such a long process because you have to change a whole set of regulatory dimensions that govern ICE, you have to change the law in a number of different ways,” he said.

Still, Young said he understands why some students may be worried after this year's election.

“It is our obligation, our passion, our goal to provide a supportive, safe environment for our students to thrive,” he said. “There is nothing on the horizon that really jeopardizes that.”

Since Trump’s election, hundreds of college presidents have signed a statement in support of the Deferred Action for Childhood Arrivals program, which gives young undocumented immigrants protection from deportation and a work permit. Among the signatures are leaders from the University of Texas System, the University of Houston and Rice University.

Read related Tribune coverage:

Some undocumented immigrants brought here as kids were granted a sort of legal status by President Barack Obama. They're in a state of shock and panic now that Donald Trump has won the White House.

Marcos Valencia was raised in Indiana, but in the eyes of the law, his home is the cartel-infested state of Tamaulipas, Mexico, where he was born. Now he's stuck in Mexico, unable to return to the country where he grew up.

Matthew Watkins contributed to this report.

Disclosure: The University of Texas at Austin, the Texas State University System, Texas A&M University, the University of Houston and Rice University have been financial supporters of The Texas Tribune. A complete list of Tribune donors and sponsors can be viewed here.