Police have begun a search for a man believed to have separately attacked and indecently assaulted four women in less than a week in Sydney's west.

A 46-year-old woman said she had been followed by a man as she walked on Carlyle Street in Bossley Park on Thursday night.

The woman told police he grabbed her and tried to steal her handbag, but she was able to kick him off before he ran away.

The attack is the fourth in a string of identical assaults on nearby streets, police said.

Three women, aged 60, 45 and 25, reported being grabbed from behind, while walking between 6:00am and 8:00am during the past week.

One of the women also said the man took her bag.

Acting inspector Andrew Meznaric said described the alleged offences as "serious".

"Females being indecently assaulted is not tolerated by the community," he said.

"We see it as a very serious incident. The females involved would be quite traumatised."

Each woman has described the attacker as being of Pacific Islander or Maori appearance, in his early 20s, of average height with dark hair.

Police said it was clear he was familiar with the area and with the nearby shopping centre.

They have begun patrols of the streets in search of him.

"We're asking females in the area to be more vigilant of their surroundings," Inspector Meznaric said.

"And if they see anything suspicious or believe that they've witnessed something, to come forward police."

CCTV footage from the nearby shopping centre and bus transit way has also been analysed.

Anyone who has been a victim or who has witnessed an attack in the past week has been urged to speak to police.