Shots were fired into the air to scare away the protesters in the southern city, while air force helicopters were deployed for surveillance, they added.
The police spokesman for Rivers state, of which Port Harcourt is the capital, confirmed the protest but denied shooting or using teargas.
"Measures have been put in place to handle the situation in such a way that public peace is not disrupted and to ensure life and property are protected," Ahmad Muhammad told AFP, without elaborating.
The groups support the creation of a breakaway state of Biafra in the southeast and want the release of Nnamdi Kanu, who is believed to be a major IPOB sponsor and director of the pirate radio station Radio Biafra.
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He was arrested in October, several months after Nigeria's government ordered Radio Biafra to be taken off air for allegedly broadcasting "unsavoury hate messages".
A previous unilateral declaration of secession to create the Republic of Biafra sparked a brutal civil war in Nigeria from 1967 to 1970.
The demand for Kanu's release has stirred up more protests across states in the region in the past days.
Since the end of the civil war, which left more than one million dead, many from starvation and disease, there have been sporadic attempts to revive the Biafra movement.