Nigerians have been reacting angrily on social media to a draft bill being discussed in the Senate which aims to "prohibit frivolous petitions".
Tweeters have been using #NoToSocialMediaBill to campaign against the proposal.
It proposes a sentence of up to seven years in prison or $25,000 (£16,000) fine for anyone who intentionally propagates false information.
Human Rights Watch condemns the move as an attempt to muzzle free speech.
Millions of social media users in Nigeria, as well as those sending text messages, could be affected, it says in a statement.
What the bill proposes
Up to seven years in prison or $25,000 (£16,000) fine for "anyone who intentionally propagates false information that could threaten the security of the country or that is capable of inciting the general public against the government through electronic message."
Up to years in prison or $10,000 (£6,000) fine or both for anyone disseminating via text message, Twitter, WhatsApp, or any other form of social media an "abusive statement"
This also involves messages intending to "set the public against any person and group of persons, an institution of government or such other bodies established by law."
Activists see the bill as an attempt to target critics of lawmakers and politicians.
The BBC's Nasidi Adamu Yahya in the capital, Abuja, says Nigerian MPs often come under the media spotlight because of the huge money they earn.
However, Senator Bala Ibn Na'allah of the governing All Progressive Congress, who sponsored the bill, said the publication of false stories was becoming rampant in the country.
"You can't write false stories just because it is social media," he told the BBC Hausa service.
The offences the proposed bill seeks to criminalise already exist under Nigerian laws including those on treason, defamation, and libel, our reporter says.
Nigeria has a vibrant civil society who use social media, and it has the largest number of mobile phone users in Africa.