Interpol has issued an international arrest warrant for a Canadian man suspected of dismembering a male murder victim and mailing body parts to political parties.

Canadian police are meanwhile trying to determine if the same man was responsible for a grisly online video of a beheading.

Montreal police said they believe the suspect, Luka Rocco Magnotta, has fled Canada as they continue to search his apartment in the city.

Police have said a janitor found a headless, limbless torso stuffed into a suitcase in an alley behind the building.

Local police would not confirm a report in the Journal de Montreal newspaper that the 29-year-old Toronto native flew to Europe at the weekend using a false name.

Police have said Mr Magnotta knew his victim, like him a white male, but gave no indication as to a motive.

Mr Magnotta, who has no criminal record, also uses the names Eric Clinton Newman and Vladimir Romanov, police said.

The first clue in the case came on Tuesday when the governing Conservative Party headquarters in Ottawa received a severed left foot in the mail.

Ottawa police then intercepted another package addressed to the Liberal Party containing a severed left hand.

Police said they believe the torso found near his apartment belongs to the same victim as the mailed body parts, and say some parts are still missing.

Investigators combed through Mr Magnotta's abandoned Montreal apartment yesterday.

One senior officer said it was the worst crime scene his force had ever seen.

Canadian media reports described a bloody mattress and pools of blood on the floor and in the refrigerator.