A group calling itself the George Nkencho coalition has handed in a list of demands to gardaí, including an independent public inquiry into the Dublin man's fatal shooting last December.
Mr Nkencho (27) was shot dead by the Garda Armed Support Unit outside his home in Clonee shortly after he assaulted a shop worker.
He was armed with a kitchen knife and, according to his family, had been suffering from mental health issues in the months beforehand.
A Garda Ombudsman investigation into the shooting is currently ongoing but supporters of the Nkencho family are demanding a full, independent inquiry.
Members of the George Nkencho Coalition gathered outside Blanchardstown Garda Station on Tuesday morning, where they called for a "transparent, thorough and fair" investigative process and demanded that the gardaí involved in the shooting be suspended from normal duty until the inquiry is complete.
Their list of demands included that any inquiry examine de-escalation measures which could be used to demobilise suspects in stand-offs in the future. It should also examine issues of bias and racial profiling in Irish policing and any deficiencies in how gardaí deal with mentally ill people.
The actions of Mr Nkencho in the shop on the day of his death did not make it right to kill him, the group said in a statement.
“How many young men and women in our community have got into scrapes and conflicts and trouble with gardaí at some point? They don’t deserve to get shot five times for it.
In this case de-escalation of the situation should have been the action taken by gardaí.”
The group said Mr Nkencho’s’s killing shows the gaps in the State’s mental health services. It said the Government must fund free psychotherapy assessments for young people “and indeed anyone who might be struggling with mental health issues.
The group said it does not believe the Garda generally employs racist policing methods but that “we need to be vigilant to ensure that racial biases are not allowed to flourish and subsequently form a new policing culture.”