The Kenya National Commission on Human Rights (KNCHR) has said it is investigating allegations of human rights violations during Monday's demos.
In a statement on Monday, the body said it was following up on the reports of vandalism, arrests, injuries and allegations of the use of live bullets by police officers.
It called on the Independent Policing Oversight Authority (IPOA) to launch a probe on the same.
It also urged the IG of police to restrain from any use of live bullets against protesters, noting that it amounted to excessive force.
Acknowledging that the police had declared their stand on the demonstrations, KNHCR however noted that officers should adhere to the checklist on public order management during protests.
Nairobi Police commander Adamson Bungei had declared the protest illegal and not allowed.
"The standards are very clear and must therefore be followed to the spirit and letter as enshrined in the Kenya Constitution and Police Service Standing Orders," KNHCR said.
"Police officers should be able to isolate and arrest violent protesters who are in breach of peace and at the same time protect those who are innocent during the demonstrations."
KNHCR reiterated that officers should act in a professional manner in defusing tension during picketing.
The human rights body further said detained protesters are to be treated in a humane way, and their rights respected.
At the same time, it warned demonstrators who turned to vandals and harmed others, saying this amounted to criminal offences.
Monday's demonstrations attracted numbers in regions including Nairobi, Kisumu and Migori.
The Commission assured that it will continue to monitor the ongoing situation.
"The Commission further affirms that any human rights violation or abuse in the context of these demonstrations must be investigated promptly, thoroughly and impartially," it said.