At least 22 people were killed and 27 others injured in a stampede on a crowded pedestrian bridge connecting two railway stations in Mumbai during Friday morning's rush-hour, police in India said.

The stampede was triggered after falling concrete hit the overpass railing, leading people in the crowd to surge forward to escape because they feared the bridge would collapse, Mumbai police official Gansham Patel said.

People had been crowding under the canopy covering the footbridge to escape heavy rain, making the deadly tragedy worse, said Shaina Nana Chudasama, of the governing Bhartiya Janata Party.

Commuters also often complain about street-sellers hawking their wares on the narrow overpass.

The pedestrian bridge connected two local Mumbai railway stations - Elphinstone and Parel.

Deadly stampedes are fairly common during Indian religious festivals, where large crowds gather in small areas with few safety or crowd control measures.

As Mumbai police appealed to citizens to donate blood to help the injured, Prime Minister Narendra Modi expressed his condolences to the families of those killed.

"Prayers with those who are injured," he tweeted.

Railways Minister Piyush Goyal said the incident was being investigated.

In a separate stampede in the southern city of Banglaore, two people were killed as hundreds jostled to obtain coupons for free food offered by a local philanthropist, police said. The philanthropist has been detained for questioning.