The victim, identified as Fahim Saleh, was found at around 3.30pm on Tuesday inside his luxury seventh floor apartment on the Lower East Side in Manhattan. There have not been any arrests in connection with Saleh's death.

A relative called police after going to check on Saleh and making the gruesome discovery.

Responding officers discovered a clothed torso, bags containing a head and arms and the electric saw in the living room, police said on Wednesday.

Investigators also recovered security video showing Saleh exiting an elevator that leads directly into the full-floor, two-bedroom apartment earlier on Tuesday afternoon closely followed by someone dressed entirely in black, including a mask, according to a law enforcement official who was briefed on the case.

It also shows a struggle between the two ensuing at the entrance to the apartment, said the official.

Police believe the relative may have interrupted the intruder before that person fled out a back exit.

The medical examiner ruled the death a homicide after an autopsy found the cause of death was multiple stab wounds to the body.

Saleh was the chief executive officer of a ride-hailing motorcycle startup called Gokada that began operating in Nigeria in 2018.

The company confirmed his death on Twitter on Wednesday and said, "Fahim was a great leader, inspiration and positive light for all of us."

Investigators were exploring whether the killing could have been related to Saleh's business dealings. They also were checking security camera video from the neighbourhood to try to locate the suspect.

Saleh's LinkedIn biography described him as a self-taught businessman who founded Gokada building on his experience of first "seeing an opportunity in his parent's native country of Bangladesh" and starting that country's largest ride-sharing company. It said he also was invested in a similar venture in Colombia.

Apartments in the 10-storey building where Saleh's remains were found sell for more than $US2 million. The building was completed in 2017 as part of a wave of gentrification in the neighbourhood.

Australian Associated Press