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).
President Muhammadu Buhari disbanded Sars on 11 October. But protests have continued, with demands for more changes in the security forces, as well as reforms to the way the country is run.
Witnesses have told the BBC what they saw when men in military camouflage opened fire on Tuesday evening.