O.P. Singh, the chief of police in Uttar Pradesh state, said the latest deaths have increased the death toll in the state to nine. "The number of fatalities may increase," Singh said.
He did not give further details on the latest deaths.
Police said that over 600 people in the state have been taken into custody since Friday as part of "preventive action."
Protesters are angered by a new law that allows Hindus, Christians and other religious minorities who are in India illegally to become citizens if they can show they were persecuted because of their religion in Muslim-majority Bangladesh, Pakistan and Afghanistan. The law does not apply to Muslims.
Critics have slammed it as a violation of the country's secular constitution and label it the latest effort by Prime Minister Narendra Modi's Hindu nationalist-led government to marginalize India's 200 million Muslims. Modi has defended the law as a humanitarian gesture.