Columbia University has threatened student protesters with "clear consequences" after protesters occupied a building in an escalating standoff. Students defied a 2 p.m. deadline to disperse Monday.

Students occupying the building face expulsion, the university warned.

"We made it very clear yesterday that the work of the University cannot be endlessly interrupted by protesters who violate the rules. Continuing to do so will be met with clear consequences. Protesters have chosen to escalate to an untenable situation—vandalizing property, breaking doors and windows, and blockading entrances—and we are following through with the consequences we outlined yesterday," Columbia said in a statement.

Students who did not commit to the terms Columbia's proposed agreement to vacate the encampment by 2 p.m. Monday have been suspended.

"Those students will be restricted from all academic and recreational spaces and may only access their individual residence. Seniors will be ineligible to graduate," Columbia said.

"This is about responding to the actions of the protesters, not their cause," Columbia said.

Columbia University said it has limited access to its Morningside campus except to students residing in seven residential buildings, labs and employees who provide essential services.

The school has also limited access into and out of the building to one gate, closing all other campus entry points.

The restrictions will remain in place "until circumstances allow otherwise," Columbia said.

New York Police Department officers said they would not enter the property unless Columbia requests it, or there is an imminent threat.

Virginia Tech said it has cleared an encampment on campus and arrested 82 protesters for trespassing, after refusing to comply with university policies.

"Virginia Tech strongly supports free speech, even when the content of that speech may be disagreeable to some. However, those rights do not extend beyond the point where they interfere with the rights of others, violate our policies, the Code of Virginia, or federal laws and/or create a threat to safety for others," Virginia Tech President Tim Sands said in a statement.

Meanwhile, Virginia Tech Muslim Student Association said in a letter the 91 students faculty and staff were arrested for peacefully protesting.

"As we reach the end of the semester, 7 months after Oct. 7, we are finding our voices still unheard. We are waiting for your support of us and Palestine," the Virginia Tech MSA said in a statement.

-ABC News' Nadine El-Bawab and Kerem Inal

California State Polytechnic University, Humboldt said it has cleared two campus buildings that had been occupied by protesters for over a week and arrested 25 people.

"Those arrested faced a range of different charges depending on individual circumstances including unlawful assembly, vandalism, conspiracy, assault of police officers, and others. In addition, students could face discipline for conduct violations while any University employees arrested could face disciplinary action," Cal Poly said in a statement.

The university called the occupation of the two buildings "criminal activity" and said there were "serious concerns it would spread even further on campus."

"This morning’s enforcement action was determined to be necessary to restore order and to address the lawlessness and dangerous conditions that had developed. What was occurring was not free expression or a protest," the university said in a statement.

The campus will remain closed until May 10.

Columbia University announced Monday it will not hold a campuswide commencement ceremony on May 15 as originally scheduled.

Columbia will focus on the smaller, school-based ceremonies instead based on "input and feedback from student leaders," the school said.

"Our students emphasized that these smaller-scale, school-based celebrations are most meaningful to them and their families," the school said in a statement. "They are eager to cross the stage to applause and family pride and hear from their school’s invited guest speakers."

The smaller school ceremonies will begin on Friday. Columbia said it may hold "a festive event" on May 15 instead. Security concerns were among the reasons the larger ceremony was canceled.

One of the reasons Columbia said it had called in the New York Police Department last Tuesday was in order to make room for the schoolwide ceremony in the same location as the encampment.