Students from Delhi University display placards and shout slogans during a demonstration to condemn police firing on a crowd in Ranchi on Saturday. AFP

Anger has engulfed the Islamic world since last week, when a spokeswoman for Prime Minister Narendra Modi’s party commented on the relationship between the prophet and his youngest wife on a TV debate show.

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Muslims took to the streets after Friday prayers in huge numbers across India and neighbouring countries to condemn the remarks, with police firing on a crowd in the eastern city of Ranchi.

A policeman aims a handgun at demonstrators during a protest against Nupur Sharma in Ranchi. AFP

"Police were forced to open fire to disperse protesters... resulting in the death of two," a police officer from the eastern city of Ranchi told the media.

Officers said that the crowd had defied their orders not to march from a mosque to a market and thrown broken bottles and stones when police attempted to disperse the rally with a baton charge.

An effigy depicting former BJPspokeswoman Nupur Sharma is displayed during a demonstration in Karachi. AP

Authorities cut internet connections in the city and imposed a curfew, with local resident Shabnam Ara telling the media the atmosphere remained tense on Saturday. "We are praying for peace and harmony," she added.

Police in Uttar Pradesh fired tear gas to disperse at least one rally after several demonstrations were staged across the northern state.

Most protests ended peacefully but demonstrators in some cities had thrown stones at police and injured at least one officer, said Avanish Awasthi, a senior government secretary in the state.

"We will take strict action against those indulging in stone pelting and violence," Awasthi told reporters.

"Those working behind the scene, instigating violence, will not be spared at all."

Prashant Kumar, a senior police officer in the state, told the media that up to "136 protesting miscreants" had been arrested from six districts around Uttar Pradesh.

Cities around India saw sizable demonstrations on Friday, with some crowds burning effigies of Nupur Sharma -- the Bharatiya Janata Party (BJP) spokeswoman whose comments set off the furore.

Agence France-Presse