Police arrested at least 400 suspected rioters during unrest in several states.
Leaders of prominent Islamic groups and mosques in the country have appealed to fellow Muslims on Monday to suspend plans for protests against derogatory remarks about the Prophet Muhammad made by two members of the BJP.
The message to avoid big gatherings was circulated after demonstrations took a violent turn last week, leading to the death of two teenagers and the wounding of more than 30 people, including police.
"It is the duty of every Muslim to stand together when anyone belittles Islam but at the same time it is critical to maintain peace," said Malik Aslam, a senior member of Jamaat-e-Islami Hind, a Muslim organisation that operates in several states.
Early this month, two senior members of the BJP made remarks that offended Muslims. A party spokeswoman made the offending comment in a television debate and a party spokesman on social media.
The party suspended both of them and said its denounced any insult towards any religion, and police have also filed cases against the two, but that did not stop enraged people taking to the streets in protest.
Police arrested at least 400 suspected rioters during unrest in several states and curfews were imposed and internet services were suspended in some places.
Authorities in Uttar Pradesh on Sunday demolished the home of a man linked to the riots, drawing condemnation of the state government, led by the BJP, from constitutional experts and rights groups.
Muslims and rights groups interpreted the destruction of the house as punishment for the riots but state authorities said it was because it was illegally built on public land.
"We are not demolishing houses to stop Muslims from protesting as they have all the right to take to the streets," an aide to Chief Minister Yogi Adityanath told Reuters.
PM Modi has not commented on the controversial remarks that sparked the protests even as condemnation grew abroad.
Countries including Qatar, Saudi Arabia, the UAE, Oman and Iran, important trade partners for India, have lodged diplomatic protests.