Police believe one man is responsible for at least three indecent assaults on teenage girls in the Perth CBD — and he remains on the run.

Detectives are continuing to investigate several reports that a man had approached and indecently assaulted girls in Murray Street, Wellington Street and the Watertown Outlet shopping centre.

Each of the allegations relates to incidents that occurred during the day — between 2.30pm and 4pm on Monday, March 23, and Tuesday, March 24.

WA Police have launched a public appeal to assist in finding the man, believing he may have information to assist with this investigation.

Detectives urge anyone who recognises the man, or who has experienced a similar approach, to call police on 131 444.

Information can also be provided to Crime Stoppers on call 1800 333 000 or online here. People can remain anonymous.