In a statement, David Kaye also urged authorities to revoke other measures that restrain access to internet and social media and curtail the freedom of the press.
He says the amendment, passed last month, is ambiguous and imposes harsh penalties for a wide range of legitimate expression.
Nauru’s government says its internet restrictions, which includes blocking Facebook, is to limit pornography, crime and cyberbullying.
But Kaye says he’s concerned that the restrictions are instead designed to prevent asylum seekers and refugees on the island from sharing information about their situation.
He says freedom of the press is also limited by prohibitive visa fees for foreign journalists, which he says is problematic in a small country with limited media.
Earlier this month, the UN Subcommittee on the Prevention of Torture visited Nauru to focus on the situation of people being detained on the island and the need to establish an independent monitoring body for places of detention.