Police have fought off protesters at a Melbourne building where Prime Minister Tony Abbott is inside.

The university student protesters angry at university cuts yelled “shame” at police officers and clashed as the officers tried to get inside the Melbourne University building.

A demonstrator earlier told protesters Mr Abbott entered the building from the other side and claimed police “assaulted” protesters, leading to chants of shame.

Mr Abbott is officially opening the Peter Doherty Institute for Infection and Immunity.

There are up to 200 protesters shouting slogans and calling for education for all and no cuts to education.

About 40 officers formed a wall guarding the entrance to the building on Friday morning.

Up to 20 police officers are guarding another entrance.