Around 5,000 supporters of Tehreek-e-Labbaik Pakistan -- a previously banned group -- gathered to protest in the city centre calling on the government to take stronger action against India over the comments.
"The Prophet of Islam is our red line. Be it India... or anyone else, they should know that defenders of Islam will not remain silent," said school teacher Irfan Rizvi.
Members of India's 200 million-strong Muslim minority community staged demonstrations in several cities, with a large crowd gathered on the steps of the 17th-century Jama Masjid mosque in New Delhi.
Elsewhere in the capital, social media footage showed students of the prestigious Jamia Millia Islamia university burning an effigy of Nupur Sharma -- the Bharatiya Janata Party spokeswoman whose comments set off the furore.
Authorities in Indian-administered Kashmir cut the restive territory's internet connections, restricted prayer congregations at mosques and imposed a curfew on Friday.
A spontaneous shutdown saw businesses close across Srinagar, the region's major city, with protesters calling for retribution against "disrespect" to the prophet.
And in Indonesia, the world's largest Muslim-majority country, about 50 protesters staged a rally in front of the Indian embassy in Jakarta.
"The Indian government must apologise to Muslims and they must take strict action against the politicians who made the remarks," protest coordinator Ali Hasan told AFP.
