The 149-minute movie released in 1,000 screens without trouble, including in Delhi, industry sources said.
Security was, however, particularly high at cinema halls in Uttar Pradesh and Mumbai over fear of protests by Muslims.
The original Tamil-Telugu "Vishwaroopam" was banned in Tamil Nadu last month for 15 days after 24 Muslim groups objected to certain scenes of the film as derogatory to their community.
The controversy surrounding the movie, whose story revolves around an Al Qaeda plot and an Indian couple in the US, seems to have sparked increased interest among viewers in north India.
In Delhi, the spectator response was "okay" but the collections could pick up over the weekend, said Anant Verma, director and business head, DT Cinemas.
"Whoever has seen the movie has liked it, be it people from south or north India," Verma told IANS.
"The publicity the movie got is working in its favour. We are expecting a hike (in collections) over the weekend."
He said there had been no security issue at any of his halls in Delhi, and "everything is under control".
"The occupancy for the first show was 55-60 percent but that is how it is every Friday," he said.
Delhi-based distributor Joginder Mahajan admitted that "Vishwaroop's" start was poor but "it is expected to improve over the weekend".
He pointed out that if a film runs into controversy, people avoid it on the first day.
In East Punjab, a film distribution area, the opening was below average, said distributor Jaspal Dhingra of Nanaksar Enterprises.
"The film may be good but collections are very average. Generally dubbed films from south India don't do well in Punjab. There are very few people here who want to watch the movie," Dhingra told IANS.
"As far as security is concerned, there were no issues here," he said.
Written, directed and produced by Kamal Haasan, the Rs.95 crore thriller was set for release in Tamil and Telugu Jan 25. A day earlier, the Tamil Nadu government imposed a two-week ban on the film.
Subsequently, Kamal Haasan, who also stars in the lead role, agreed to make some cuts. Talks between his representatives and Muslim outfits have taken place in Chennai.
There were no protests in the Rajasthan capital too, said officials.
Small theatres in Mumbai were packed but multiplexes lacked enough audience for "Vishwaroop".
"Theatres with 150 seats are almost full. But in big theatres with 1,000 seats have hardly any crowd," Manoj M. Desai, executive director of G7 Multiplex, told IANS.
"I feel there is so much police protection around that the audience feels 'Why take a risk?'" said Desai.
In Lucknow, the film was screened in five multiplexes and two single-screen theatres, officials told IANS.
There were minor protests outside Shubham Hall in Lucknow and a multiplex in Agra.
Atul Gupta, deputy manager of PVR Cinemas in Lucknow, told IANS that the first show had only 70 spectators in a hall meant for 209.
Kamal Haasan said Thursday that he had incurred a loss of Rs.30-60 crore because of the delays in the movie's release in Tamil Nadu.
The film has also been banned in Qatar, the UAE, Malaysia, Singapore and Sri Lanka. But it has released in the US and Canada.