Police in India's Mumbai city have opened an investigation into the murder of a woman, allegedly by her live-in partner of three years.

They say 32-year-old Saraswati Vaidya's body was found in her apartment in Mira Road district on Wednesday.

Police have arrested her partner Manoj Sane, 56, on charges of murder. They allege he "brutally killed" Vaidya and dismembered the body.

Mr Sane is in custody and has not yet made any public statement.

Warning: This story contains details some may find distressing

Police say they reached Mr Sane's apartment on Wednesday evening after some residents of the building complained of "a foul smell" coming from the house.

Inside the apartment, they found Vaidya's decomposed body, which had been cut into multiple pieces.

"We are investigating the motive behind the murder and how he executed it. We believe that he cut the woman's body into pieces to make it easy for him to dispose them off," Deputy Commissioner of Police Jayant Bajbale told Hindustan Times newspaper.

Police suspect the murder was committed two-three days ago and have taken samples for a forensic analysis.

"The situation is deeply troubling, and we are committed to finding justice for Vaidya," Mr Bajbale told reporters.

The murder is making headlines in India, mostly because it comes just seven months after another man - Aftab Poonawala - was arrested on allegations of murdering his live-in partner in a similar manner.

Police alleged that Mr Poonawala, 28, murdered 27-year-old Shraddha Walkar last May, chopped up her body into dozens of pieces, stored them in his home fridge and then went around disposing them off in different parts of the city.

The case - dubbed as "fridge murder" - dominated headlines in India for weeks because of the sensational claims by the police.