A man who ran away bleeding after the third woman he stalked in North Sydney over one afternoon hit him in the head with a saucepan appeared in court on Saturday.

Akram Khan, 23, of Oxley Park was denied bail at Parramatta Bail Court over charges of stalking three women and assaulting one of them from a series of incidents on April 9.

The police fact sheet tendered to the court said that Mr Khan followed a 36-year-old woman home after she got off a bus on Blue Street, North Sydney about 6.05pm.

She was carrying her handbag and a large stainless steel cooking pot she was bringing home from work.

The fact sheet said the woman heard someone walking close behind her on Dumberton Street, McMahons Point and became concerned for her safety.

Police allege the woman felt someone walking very close behind her as she got to the outside glass door of her unit complex.

"The victim became fearful and tried to walk back out of the glass door, but the accused was standing 30 centimetres away from her when she turned around," the fact sheet said.

As she walked past, police allege Mr Khan grabbed her, pulled her back into the building and covered her mouth with his hand.

The fact sheet said the woman was "extremely frightened" that Mr Khan would sexually assault her so she hit him over the head with the saucepan.

"He still had his hand over her mouth, so she swung her arm and hit him again and after this he let go," the fact sheet said.

Mr Khan was bleeding from a cut on his head as he ran away, police said.

Police allege Mr Khan had also followed a 23-year-old woman from Milsons Point train station to an office building on Alfred Street at about 4.35pm.

The fact sheet said he then followed her down the street and at one stage ran ahead of her, hid in a doorway and peeked out to watch her.

The victim told officers Mr Khan had walked very closely behind her on the street and tried to touch her hair.

Police allege Mr Khan also followed a 36-year-old woman who was going back into work after a cigarette break in front of an office building on Miller Street, North Sydney at about 5.30pm.

He got into the lift with the woman and then tried to get into a locked door to her workplace, the fact sheet said.

Police arrested Mr Khan at his Oxley Park home on Friday following an investigation.

Mr Khan applied for bail on Saturday but the prosecution opposed it due to the threat police allege he posed to the community.

His legal aid solicitor said that he would be willing to agree to strict conditions which would amount to "house arrest".

But the magistrate said he denied bail due to the seriousness of the offences and for the protection of the public.

Mr Khan is due to appear at Central Local Court on July 8.