ZURICH/LAUSANNE (Reuters) - Police began dispersing pro-Palestinian protesters at the Swiss university of ETH Zurich on Tuesday, management said, after student demonstrations spread to campuses in several cities.

Students set up camp at Lausanne University (UNIL) last week and protests have since spread to at least three more sites in Zurich, Geneva and Lausanne.

"ETH Zurich sees itself as a place where different opinions and perspectives can and should be expressed openly. However, unauthorised actions are not accepted at ETH Zurich," ETH university said, adding that protesters had been repeatedly asked to leave the building before police arrived.

Video footage of the protest on social media earlier showed seated protesters with keffiyehs and Palestinian flags chanting "free, free Palestine" and "viva, viva Palestina".

Protests also began in University of Geneva and the Ecole Polytechnique Federale de Lausanne on Tuesday, according to students' social media posts.

At UNIL, hundreds of students chanted "we are all the children of Gaza" on Monday as a single security agent looked on. Management asked them to move, a UNIL statement showed, but they remained in the building on Tuesday.

Some academics have sided with students.

"We consider the steps they've taken to be peaceful and good natured aimed at bringing to the public's attention a dramatic situation," UNIL political science professor Bernard Voutat said on Monday. "We teachers cannot remain silent."

Police have dispersed protesters at other universities across the world including Columbia University in New York, and the Sorbonne in Paris.

(Reporting by Emma Farge and Dave Graham; Editing by Alison Williams)