Melbourne's reputation for tolerance has taken yet another battering, after a shocking racial attack on a city bus.

Two Indian women were abused and assaulted, their attacker even chased them when they tried to escape.

In Bay Street Port Melbourne, two young Indian sisters boarded a bus, but trouble started before they'd even reached their seats.

Police said one of the women was carrying a handbag and managed to accidentally knock the other woman with her bag.

“She's turned around to apologise to the woman and that's when the abuse has then started on the bus,” Senior Sergeant Steve Bills said.

The racial abuse continued during the 15 minute trip until the Indian women alighted from the bus at Queen and Collins Streets. But they couldn’t escape the abuse, in fact it got worse.

The abusive woman followed them onto the footpath, slapped them both across the face, threatened them, and smashed a mobile phone one of them was using to call the police.

The attacker and her friend then left in a cab, but the Indian media has leapt on the story, linking it to a string of earlier cases of racial abuse in Melbourne.

“We are just recovering from that now suddenly an isolated issue can create again, uneasiness within the community,” Vasan Srinivasan from the Federation of Indian Associations said.

The Premier has urged Victorians to take a stand.

“To not tolerate this themselves, and to speak up when somebody else on the public transport system is being abused,” Ted Baillieu said.

The female attacker is described as 160cm tall, with short spiky blonde hair, very solid build and what police call a "very manly" appearance.

She was wearing 3/4 pants, and a black t shirt with 'Burberry' written on the front.