Fire tore through a Mumbai building where a rooftop party was being held early on Friday, killing at least 15 people and leaving many injured, police said.

The blaze started just after midnight in a top floor restaurant in the centre of the city and quickly spread to two adjacent bars, destroying the entire building in 30 minutes, media reports said.

Most of those who died were women at a party at the restaurant, Mumbai's disaster management authorities said.

One woman who said she was in the building at the time told of the desperate scenes as people tried to escape.

“There was a stampede and someone pushed me,” Sulbha Arora said on Twitter.

“People were running over me even as the ceiling above me was collapsing in flames. Still don't know how I got out alive. Some powers were definitely protecting me.”

Television footage showed fire engines and emergency teams rushing to the scene as the building was being consumed by flames and dark plumes of smoke rose into the night sky.

“So far the deaths of 15 people have been declared,” S. Jaykumar, a Mumbai police commissioner, told reporters, adding that the cause of the fire was under investigation.

More than a dozen people were taken to nearby hospitals and two were in critical condition, civic authorities said.

Firefighter Sanjay Hiwarle told reporters the blaze was brought under control during the night and a “cooling operation” was underway.

The blaze broke out in the Kamala Mills compound, which houses restaurants and other commercial establishments including hotels, around 12.30am (local time), police said.

Several media organisations also use the building and at least three national news channels were affected by the fire, including Times network's Times Now, Mirror Now and ET Now channels.

Indian President Ram Nath Kovind expressed his condolences on Twitter.

“Disturbing news about the fire in Mumbai. Condolences to the bereaved families and wishing the injured an early recovery. Commend the valiant efforts of fire-fighters and those in rescue ops,” he said.

Accidental fires are common across India because of poor safety standards and lax enforcement of existing regulations.

A fire swept through a sweet shop in Mumbai earlier this month, sparking a building collapse which killed 12 sleeping workers.

In September, a gas cylinder exploded in an unfinished building in Mumbai killing six people.