Melbourne, Dec 21 (PTI): A "very manly" Australian woman threatened two young Indian women and slapped one across the face here in a "racial attack", prompting Victoria police to launch a probe into the assault.

The mystery woman - believed to be in her 30s - racially abused the Indian passengers "throughout the journey into the city", the police said in a statement today.

The incident took place after the Indian women - both aged in their 20s - walked down the aisle of a bus looking for a seat, one of the women accidentally bumped the Australian passenger, already seated, with her handbag on December 12.

The Indian woman turned to apologise but was racially abused by the Australian, the statement said.

"The racial abuse continued throughout the journey into the city, where the two women got off the bus at the corner of Queen and Collins streets. The abusive woman followed the two victims off the bus and physically assaulted them by slapping them across the face," it said.

The attacker slapped one woman across the face and knocked a phone from the hand of the other victim, who was trying to call police.

As the phone smashed on the ground, the attacker warned the two women not to call police before fleeing in a taxi.

Police have appealed for witnesses to come forward. The police statement described the offender as "about 160 centimetres tall, short spiky blonde hair, very solid build and looked very manly."

The ugly behaviour comes just weeks after another horrible case of racial abuse on Melbourne's public transport system made headlines.

In that incident passenger on a rail replacement bus on the Frankston line from Mordialloc to Caulfield yelled abuse and threats at some French girls on the bus who were singing a song in French.