University chiefs are seeking an injunction against 10 animal activists over its new animal testing centre.
Hundreds of protesters marched through the centre of Oxford in July
Oxford university wants the High Court in London to extend an existing 35-metre "no harassment" zone around its South Parks Road centre in Oxfordshire.
The university's legal representatives want a judge to extend the order, granted last month, until a full trial.
About 98% of the new facility's work would involve rodents, the remainder being amphibians, fish, and primates.
Solicitor-advocate Timothy Lawson-Cruttenden said: "We are being harassed or we anticipate that we may be harassed by the defendants."
He is pressing for the injunction against: Mel Broughton, John Curtin, Robert Cogswell, Speak Campaigns, Stop Primate Experimentation at Cambridge, Stop Huntingdon Animal Cruelty, Oxford Animal Rights Group, People Against Cruelty to Animals - West Midlands, West Midlands Animal Action and Animal Liberation Front.
The "no go" area extends to all the university's buildings in the city.
In July, pressure group Speak - Stop Primate Experiments at Cambridge - organised a 500-strong march to the site.
Last month, Mr Cogswell asserted the university was being "undemocratic" and said Speak's campaign would "never indulge in illegal action and would not do so in the future."
Mr Lawson-Cruttenden added: "The university does actually believe passionately in the freedom of expression and have been maintaining that right for 800 years.
"They want to ensure that law and peace are preserved in Oxford.
"They are prepared to talk to anyone about agreeing a code of practice or conduct that can balance the two rights - theirs not to be intimidated against the freedom of speech."
The university has offered to provide a demonstration area immediately opposite its facility.
However, the demonstrations would be restricted to 25 protesters and limited to four hours, Mr Lawson-Cruttenden said.
Demonstrators would also have to give police 24-hours' notice.
But weekly demonstrations, held each Thursday for the past six months, would continue.
The named defendants are contesting the injunction under the 1997 Protection from Harassment Act on the basis that there is no evidence that they are acting
The hearing was adjourned until Wednesday.