Nigeria's President Muhammadu Buhari has promised "extensive" reforms amid protests against police brutality.
He also promised justice for victims of police abuse and an investigation into the death of a protester in Oyo state.
Demonstrators have long called for the Special Anti-Robbery Squad (Sars) to be broken up.
But they remain unhappy following Sunday's announcement that officers are being redeployed to other units rather than being disciplined.
In his video address on Monday, President Buhari said disbanding Sars was "only the first step" in a range of reforms, but added that police officers were hard-working, and the reputation of the force should not be tarnished by a "few bad eggs".
Over the weekend, protests against Sars spread to Europe and Canada after reports of unlawful arrests, torture and shootings.
Demonstrations have entered their fourth day with reports of protesters barricading a major road in the commercial hub of Lagos, and others gathering close to the city's main airport.
In a statement, Nigeria's police chief Mohammed Adamu said allegations of abuse would be investigated by a committee including civil society members.
Yet many are concerned at suspected wrongdoers continuing to serve in the force, and it is unclear whether any officers will be prosecuted for past abuses.
Sceptics also point to the fact this is the fourth time in as many years that promises have been made to disband or reform Sars.
After Sunday's announcement that the police unit would be disbanded, there were reports of officers continuing to use tear gas, water cannon and live rounds against protesters in the capital, Abuja, and the south-western state of Oyo, fuelling concerns that people in Sars had not been removed from duty.
It was not until musician Davido joined protests in Abuja that the police stopped arresting demonstrators.
The BBC's Ishaq Khalid in the capital says there are also fears that if thousands of Sars officers were dismissed at once they could pose a security threat.
Activists say that the abuses carried out during the protests - including beatings, intimidation and the disproportionate use of force against demonstrators - were all carried out by policemen who did not belong to Sars.
They say a total overhaul of policing in Nigeria is needed.
Source: bbc.com
