Rights group Amnesty International said at least 12 people were killed by soldiers and police in Lagos on Tuesday.
Nigeria's army dismissed the reports as "fake news" in a post on Twitter.
Authorities have imposed an indefinite round-the-clock curfew on the city and elsewhere, but some defied the order.
Protests against a police unit have been taking place for two weeks. Demonstrators have been using the social media hashtag #EndSars to rally crowds against the Special Anti-Robbery Squad (Sars).
