The president of an Ivy League university has been accused of backing his car into a student and running over a second student's foot following an on-campus debate.

The students involved in the debacle had attended a debate between supporters of Israel and backers of the Palestinian cause at Cornell University on Thursday night. 

After the event, the two followed University President Michael Kotlikoff to his car and grilled him about free speech on campus, the Cornell Sun reports.

Aiden Vallecillo, a member of Students for a Democratic Cornell, explained that he and three other members of the student-run group had not expected Kotlikoff to attend the debate. 

The event featured author and political scientist Norman Finkelstein. Kotlikoff gave an opening statement.

'We decided to converse with Kotlikoff after Finkelstein - as well as a number of student debaters and Kotlikoff, himself - encouraged the proliferation of free speech on campus,' Vallecillo recounted.

He said they were objecting to the university's suspension of student demonstrators and measures they said stifle free speech on campus.

But in an email to students on Friday, the university president alleged that students and non-students 'loudly shouted' questions at him and refused to stop recording. 

The students refute that claim.

'We weren't shouting at him - it was mostly one person who was talking with him and just trying to have a conversation,' said junior Hudson Athas.

'I feel that he violated his own proclaimed philosophy of free and open discussion and I don't believe it was anything that could remotely be classified as harassment.' 

Vallecillo also described the president as 'dismissive,' 'disinterested' and 'disrespectful' in response to their questions.

In footage posted by the student group, Kotlikoff could be seen accusing the group's president, Sophia Arnold, of having an 'agenda.'

When he then approached his car, the university president said 'good night' to the students and got in his black Cadillac SUV the students described as a 'nice car' as they continued to try to speak with him about university policy.

Video footage released by the university then showed a group of students gathered behind the car, but nobody could be seen touching the vehicle despite Kotlikoff's assertion that the group of students banged on the windows, blocked his path and shouted.

Kotlikoff claimed he waited until there was space behind him before 'slowly maneuvering' out of the parking lot.

But the footage released by the university showed just 15 seconds had passed between Kotlikoff entering his vehicle and backing out of the parking spot into Athas, who had just asked: 'Am I allowed to stand here?'

He also allegedly ran over Vallecillo's right foot, and drove away without saying anything to the student activists while Vallecillo yelled: 'You just rolled over my f***ing foot, oh my God.'

Arnold described the entire incident as alarming.

'I don't even have the words for it. I was pretty shocked and offended,' she told WSYR. 'A random pedestrian pulling out of a supermarket parking lot would probably have shown more care.'

Following the incident, the students called Cornell University police, who took statements from the students at the scene and called Cornell Emergency Medical Services.

Cornell EMS was then dispatched to the parking lot at 8.31pm, when a police scanner mentioned a 'college male' whose 'foot was run over by a vehicle,' the Cornell Sun reports.

Vallecillo said he was then seen on site by first responders, but has not received any further medical attention, though he told The Sun on Friday his foot was painful to walk on.

No charges have been filed in the incident, as Vallecillo said he feels 'fearful' and 'intimidated' about pressing charges with the Cornell University Police Department, considering Kotlikoff 'is the boss of CUPD' and has released a statement that includes 'false information about us and our actions.'

In his email to students on Friday, Kotlikoff described those involved as both students and non-students who 'are known to Cornell for their past conduct' and have 'a long history of ongoing verbal and online abuse' toward members of Cornell's administration and staff, as well as 'disruptive protest.'

Vallecillo said that characterization was a 'deliberate lie,' arguing that the four SDC members involved have 'no prior conduct record.'

Arnold also said she believes the president's statement was an attempt to control the narrative.

'It felt like he was deliberately slandering us before the university even checked on those two students to see if they were OK,' she claimed. 

In a statement to NBC News on Monday, a spokesperson for the university said it was investigating the incident and stressed that not everyone involved was a current student.

'The university will take action, as appropriate, based on the results of the investigation and in line with its policies, which are designed to uphold a safe environment for the Cornell community,' the spokesperson said.

The Daily Mail has also reached out to the university for comment.