Amnesty International Kenya, International Justice Mission Kenya, Haki Africa and the Kituo cha Sheria have filed a petition asking for monetary compensation for five victims of brutality as police enforced a Covid-19 curfew.
They have sued the inspector general of police, the minister in charge of security and the attorney general.
They accuse them of of failing to uphold their mandate while enforcing the curfew leading to loss of life, injuries and the looting of businesses.
The groups have demanded compensation of about 500,000 Kenyan shillings ($4,600; £3,600) for the five victims.
Among those represented by the rights groups is 13-year-old Yassin Moyo who was shot dead on his parent's balcony as police enforced the night-time curfew.
One police officer was charged with the murder of Yassin and is out on bail.
The other victims are Joseph Simiyu, Judith Simiyu, Daniel Waithugi Nga’nga and Jacktone Ouma Ochilo.
The government has eased some restrictions and extended curfew start time by two hours.