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.

In a letter authorizing the NYPD to enter the Columbia University campus and break up the protest, the school detailed the backstory on its recent talks with those in the encampments and the takeover Tuesday night of Hamilton Hall.

According to the letter, from Columbia President Minouche Shafik, an individual "hid in the building" at Hamilton Hall until it was closed and let others in. The group's purpose was "occupying the building," the letter read.

Two security guards were inside the building at the time, and the university said in the letter to the NYPD they were able to "secure their release."

"We believe that while the group who broke into the building includes students, it is led by individuals who are not affiliated with the University," the letter read. "The individuals who have occupied Hamilton Hall have vandalized University property and are trespassing."
Addressing the encampment on the school's Morningside campus, the university told police discussions had been carried out with group representatives, but on Sunday, they "reached an impasse."

At that time, the university says it told the group they did not have permission to "occupy spaces on campus" and were "in violation" of school rules and policies.
On Monday morning, the protesters were told they would be suspended if they didn't disperse by Monday at 2 p.m. ET.

The university said in its Tuesday night NYPD letter that those in the encampment were "suspended" and "not authorized to be on University property and are trespassing."

The university said it believed the actions of those in the protest were escalating. "These activities have become a magnet for protesters outside our gates which creates significant risk to our campus and disrupts the ability of the University to continue normal operations," the letter read.

Columbia's president concluded the letter by asking the NYPD to "help to clear all individuals from Hamilton Hall and all campus encampments."

She further asked police to have a campus presence through May 17 -- graduation is May 15 -- "to maintain order and ensure encampments are not reestablished."

Police moved onto the Columbia University campus a little before 9 p.m. ET and began making arrests.

The NYPD also used a vehicle with an extendable roof ramp to help officers breach Hamilton Hall from an upper floor. From there, the police cleared the building.

The campus encampment and hall were cleared before 11:30 p.m.

-ABC News' Jolie Lash, Aaron Katersky and Joshua Hoyos