Local villagers rushed to the accident spot and carried out rescue operations before rescue officials and fire brigade personnel from nearby Botad and Sihor towns rushed in with cranes.
Numerous injured were trapped under the twisted wreckage and had to be extracted by villagers and emergency personnel, according to Harshad Patel, the district collector.
The death toll in the accident has gone up to 30, Jadeja informed the state Assembly in Gandhinagar, adding that while 26 people died on the spot, four succumbed to their injuries at a hospital.
Authorities say the truck skidded off an expressway on Tuesday in Gujarat state in western India.
The injured were rushed to nearby hospitals for treatment.
Reports are coming that the truck was carrying almost 60 people. Initial investigations indicated that the driver had lost control, causing the lorry to swerve off the bridge and fall 8m onto a dry riverbed.
"The accident was extremely unfortunate and anguishing", Mr Modi posted on Twitter.
Vijay Rupani, Gujarat's chief minister, also expressed condolences. "May those who have been injured recover at the earliest", a tweet from the Prime Minister's office said.