Witnesses and the rights group Amnesty International were quoted by BBC saying several people were killed and wounded when soldiers opened fire.
The state governor said only one person had died while at least 25 people were wounded.
An indefinite 24-hour curfew has been imposed on Lagos and other regions.
Protests over a now-disbanded police unit – the Special Anti-Robbery Squad (Sars) – have been taking place for two weeks, with demonstrators using the social media hashtag #EndSars to rally crowds.
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