Most of the attacks in Bihar and Jharkhand states occurred before dawn Tuesday, according to officials.
In Bihar, one of India's most lawless states, suspected communist militants held at least three railway employees hostage for at least three hours as they bombed a railway station, said senior police official V. Narayanan.
The hostages were later released, he added.
In neighboring Jharkhand, rail traffic was disrupted for more than 10 hours after suspected Maoists blew up a track, said F. Toppo, an inspector at the state's main police control room.
A band of rebels also bombed a government school before dawn, but there were no casualties, Toppo said.
They set about a half-dozen communication towers afire as well, he added.
The suspected Maoists attacked for a second day Tuesday as the government planned an offensive to seize rebel-controlled areas.
The government offensive will launch in less than two weeks, initially in two of 11 rebel strongholds, Kashmir Singh, the home ministry's joint secretary for Maoist management, said Saturday.
Forces will move to eastern India -- on the border between Jharkhand and West Bengal states -- in an operation expected to last a year.
Meanwhile Tuesday, a shootout erupted between rebels and security forces in the western state of Maharashtra during voting for legislative elections.
The gunfight occurred in the Gadchiroli district, the scene of last week's killing of 17 police officers by suspected rebels, said Jay Kumar, district police chief.
India has deployed thousands of police and paramilitaries for the voting in Maharashtra and in Haryana in the north and Arunachal Pradesh in the northeast.
"An encounter (shootout) has taken place. The situation is under control," Kumar said. There were no immediate reports of casualties.
Prime Minister Manmohan Singh, who describes the Maoist insurgency as the "gravest internal security threat" to India, said the nation's fight with the rebels has fallen short of objectives.
In the name of India's dispossessed, Maoist guerrillas known as Naxalites have battled the government since the late 1960s.
They enjoy support not only in the poorest and tribal communities but also among youth and the intelligentsia, the government suspects.
Indian authorities categorize the Naxalites as hard-core, armed local guerillas and public militias.
The government estimates there are at least 10,000 hard-core armed Maoists.
"We have not achieved as much success as we would have liked in containing this menace," Singh said last month. "It is a matter of concern that, despite our efforts, the level of violence in the affected states continues to rise."
Last year, 1,591 Maoist rebel attacks killed 721 people, government officials said. About 600 people have died so far this year in more than 1,400 rebel attacks.
In addition to targeting police, alleged police informers and people they call "class enemies," the rebels are attacking infrastructure such as roads, bridges, railways, and power and telecommunication networks.
The Naxalites say they are defending the rights of the poor. They now have influence in 20 of the country's 28 states, according to the government.