The two suspected criminals allegedly killed by police officers in Eastleigh on March 30 were buried last Friday.
This was after postmortems were conducted at the City Mortuary.
Director of investigations John Kariuki on Monday said the matter is still under investigation.
He faulted “ignorant” citizens for having unrealistic expectations of the criminal justice system “wrought with unnecessary delays created by laws”.
No one has been arrested. The killings sparked condemnation from human rights groups and applause from many Eastleigh residents and traders.
The killings were captured on a video that shows a man, said to be an officer at Pangani police station, shooting one of the suspects.
Kariuki said there is a clear process to be followed – which takes time – before arrests are made.
He added, “But Kenyans expect someone to be arrested, charged and jailed immediately he or she is accused of committing an offence. The problem in this country is laws are read by lawyers, police and judiciary officers.”
Kariuki said the investigation file must be forwarded to Director of Public Prosecutions Keriako Tobiko for directions.
A senior officer at the Pangani police station said more than 15 officers from the DCI carried away the occurrence book, statements recorded from witnesses and all the material gathered by the station on April 2.
The officer, who sought anonymity, said detectives also swept the scene for evidence the same day.
Kariuki said he cannot state when detectives will complete investigations.
He said divulging information may jeopardise the probe.
“Investigations involve many things, sometimes starting all over again,” Kariuki said. He said the laws should be amended to ease burden of proving criminal cases.