Emergency workers pulled two bodies from the rain-swollen river but were still searching for the others feared swept downstream following the accident south of Mumbai overnight on Tuesday.
Television footage showed large chunks of the British-colonial era bridge had fallen into the Savitri river, but there was no sign of the vehicles in the water.
The bridge is about 170 kilometres (105 miles) from Mumbai along a major highway connecting India’s financial capital with the tourism state of Goa.
“Two bodies have been recovered by rescue agencies. We are trying to ascertain their identities and the (rescue) operations are on,” Sanjay Patil, police superintendent of Raigad district where the accident occurred, told AFP.
More than 100 rescuers armed with diving and other specialist equipment were scouring the river, but their efforts were hampered by the fast current and incessant rain.
“The flow of currents is very strong, making it difficult to launch a full-scale search operation. We are looking for vehicles and bodies over a stretch of eight kilometres,” disaster management chief O.P Singh told AFP.
“Our team is equipped with deep divers and life-saving equipment,” he said.
The air force, navy and coastguard have deployed helicopters to survey the river, while television footage showed rescuers in inflatable dinghies trying to manoeuvre on the fast-flowing water.
Home Minister Rajnath Singh told parliament that 112 rescuers in total along with divers and 12 boats have been deployed to the site.
“The central government is with the state government in this hour of crisis,” Singh said.
Devendra Fadnavis, chief minister of Maharashtra state of which Mumbai is the capital, said the bridge appeared to have collapsed after being pounded for days by the flooded river.
“The primary reason seems to be the high pressure caused due to flooding of River Savitri due to heavy rains in catchment of Mahabaleshwar,” he said on Twitter.
The incident is the latest in a string of deadly accidents in India, where enforcement of safety rules is weak and substandard materials are often used.
In April an under-construction flyover collapsed in the eastern city of Kolkata, killing 26 people.
Scores of people die every year from flooding and landslides during the annual monsoon rains in India and neighbouring Nepal and Bangladesh.