A Melbourne barber confronted and fatally stabbed a neighbour after rocks were thrown at his business window, a court has heard.

Tony Papadimitriou, 35, was on Thursday refused bail after the Supreme Court heard he ran from his Preston barbershop on the afternoon of July 10 to confront Donato Galgano on the other side of the street.

Police allege that about 4.40pm Mr Papadimitriou stabbed Mr Galgano with a knife. The 68-year-old, who had been holding a saucepan, collapsed and died at the scene.

Mr Papadimitriou is charged with murder.

Detective Senior Constable Miranda Stubbs told the court witnesses saw Mr Galgano and Mr Papadimitriou in an altercation about 1pm that day, and that Mr Galgano threw rocks at the barbershop window at 4.08pm and 4.12pm.

On either side of those alleged incidents, Mr Galgano called triple zero asking for police help. In one call, the court heard, he claimed Mr Papadimitriou had thrown the rocks and that 'he's crazy.'"

Police were again called when witnesses saw Mr Galgano collapse.

Detective Senior Constable Michael Howard said a CCTV camera in the barbershop captured Mr Papadimitriou running out of the shop and crossing the road towards Mr Galgano. The alleged stabbing was not captured on camera, the court heard.

Detective Senior Constable Howard said Mr Papdimitriou went to his nearby home after the alleged stabbing and a CCTV camera there captured him entering the home before he came out and looked in the direction of Mr Galgano.

A pocket knife was found in Mr Galgano's pocket and a folding knife was found in Mr Papadimitriou's bedroom, the court heard. Both knives had blood on them.

Defence counsel Nick Papas, QC, said Mr Papadimitriou applied for bail so he could save his business from closure and care for his ill father.

Mr Papadimitriou had mental-health problems, the court heard.

But Justice Betty King said the bail application did not meet the threshold for extraordinary circumstances, and ruled there appeared strong evidence the accused killed Mr Galgano.

Mr Papadimitriou, who cried at several points during the hearing, is due to front Melbourne Magistrates Court in October.