He had earlier said that five injured were rushed to hospitals and 10 bodies were handed over to their family members after post-mortem.
Most of the passengers were from other states like Uttar Pradesh, Madhya Pradesh, Rajasthan and Assam. "The driver of the bus lost control over the vehicle and it plunged into the river after breaking the railing of the bridge".
Most of the people died due to drowning including the bus driver, he said.
The bus was brought out of the river with a crane.
"The death toll in today's tragic accident has risen to 33", a senior local government official Kailash Chand Verma told Xinhua over telephone from Sawai Madhopur.
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The bus was carrying people to a Hindu temple when the accident occurred around 7:30 a.m. Saturday.
Police did not release any information on what caused the accident.
Prime Minister Narendra Modi said in a statement that he was "anguished" by news of the crash. "Rescue operation is underway to find any survivors", Subhash Mishra, CO, City said.
Rajasthan Chief Minister Vasundhara Raje took to Twitter to express her condolences and support for the victims.