In the capital New Delhi, hundreds of protesters waved placards and shouted slogans near the parliament while others burnt an effigy of Prime Minister Manmohan Singh.
Communist parties that lend crucial support to the Congress-led coalition government called the strike to demand a rollback of the price increases for diesel and gasoline.
In Agartala, capital of northeast Tripura state, public transport ground to a halt, the Press Trust of India news agency said.
Tripura is one of three communist-ruled states including Kerala and West Bengal.
The West Bengal state government ruled out a reduction in oil prices despite the strike action.
"Let Delhi bring down the prices first. Then we shall think about it," Chief Minister Buddhadev Bhattacharjee told reporters on Monday.
A key truck driver's union said thousands of trucks that carry iron ore stayed off the road Tuesday in the eastern coastal state of Orissa.
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"We will observe the 24-hour bandh (strike) till tomorrow morning. Some