Professor Louise Richardson, who took charge of her new post recently, said she was comfortable with institutions giving platforms to extreme speakers as it is the best way to challenge their views.
"We need to expose our students to ideas that make them uncomfortable so that they can think about why it is that they feel uncomfortable about and what it is about those ideas that they object to," she said.
Six universities are currently being investigated over allegations that they allowed meetings to be held on campus during which Cage speakers, unopposed, advised students how to avoid being de-radicalised by the UK government's anti-terror Prevent strategy.
Richardson has expressed concerns over the Prevent duty, which requires teachers to spot radicalisation among students, because she worries "Islamic students would feel they are suspect".
"The Prevent legislation is not explicitly anti Islamist but it's widely perceived to be directed against extreme Islamists and I worry that Islamic students would feel that they are suspect. I have reservations about prevent but of course we will abide by it."
Richardson, who until late last year was vice- chancellor at St Andrews University, spent her first Sunday in her new city figuring out the location of the 38 colleges that make up the totality of Oxford University.