The government announced on Friday it was suspending Twitter’s operations in the country.
Mobile phone networks blocked access after being ordered to do so, but some users are getting around the ban.
The move comes after Twitter deleted a tweet by President Muhammadu Buhari for breaching the site’s rules.
Some users saw his post, which referred to Nigeria’s civil war four decades ago, as a veiled threat towards a secessionist movement in the south-east of the country
His government said on Saturday the tweet’s removal was “disappointing”, but not the only reason for the “temporary” suspension.
“There has been a litany of problems with the social media platform in Nigeria, where misinformation and fake news spread through it have had real-world violent consequences,” the government said.
Twitter said the announcement of a ban on Friday by Information Minister Lai Mohammed was “deeply concerning”.
The move also brought widespread condemnation from human rights groups and international powers, who say it will limit free speech in Nigeria.
In a statement, Justice Minister Abubakar Malami said he had “directed for the immediate prosecution of offenders of the Federal Government ban on Twitter operations in Nigeria”, telling the public prosecutor to “swing into action”.
The message was targeted at both corporations and individuals, the minister’s spokesperson Umar Gwandu told the BBC.
The government of Nigeria alleges that Twitter was being used to undermine “Nigeria’s corporate existence”.
The platform was allowing “the spread of religious, racist, xenophobic and false messages” that “could tear some countries apart”, a spokesperson said.
The national broadcasting regulator, NBC, had been told to begin “licensing all internet streaming services and social media operations in Nigeria”, a government statement said.
Earlier, the professional body of Nigerian mobile phone operators – known as Alton – confirmed they had been told to stop people from getting on to Twitter. The group said its members had complied with the government order due to “national interest provisions” in Nigerian telecoms law and licensing terms.
But Alton also said that it backed the UN’s position that the right to communicate both offline and online should be protected.