The violence came after a month of relative calm in the Nandigram, an area in West Bengal state, where farmers have fiercely resisted efforts by authorities to force land sales at cheap rates so an industrial zone can be set up.
On Sunday, an old woman was killed and a 9-year-old girl was injured in the gunfire. Monday's fighting left a school student with bullet injuries, Police said.
Forced land sales
At least 25 people have died in Nandigram since January this year over plans to build the industrial zone, which was to include a shipyard and a petrochemical plant.
The plan was officially abandoned in March this year after 14 people were killed in battles with police.
But sporadic violence has persisted between farmers and supporters of the communist party that has governed the state for nearly three decades and has been pushing the Nandigram project.
The farmers, who fear that forced land sales may still be being prepared, have also continued to clash with police.