The police denied any government involvement in the killings.
But UN investigator Philip Alston said that in the circumstances, suspicion was bound to fall on the Kenyan police.
"It is extremely troubling when those working to defend human rights in Kenya can be assassinated in broad daylight in the middle of Nairobi," said Mr Alston, who last week released a report accusing Kenya's police of involvement in extra-judicial killings.
Mr Kingara is one of those who gave evidence to Mr Alston.
"This constitutes a major threat to the rule of law, regardless of who might be responsible for the killings," said the UN investigator.
A student was shot dead during protests about the assassinations
Mr Alston's report called for Kenya's top policeman and the attorney general to resign for failing to address police impunity.
Mr Kingara and Mr Oulu were shot dead in their car near State House, the official residence of the Kenyan president.
Afterwards a student was shot dead in a riot sparked by the killings.
Police Commissioner Hussein Ali says three policemen have been arrested in connection with the student's death.
He said he would make a statement about Mr Kingara's shooting in a couple of weeks after a comprehensive investigation.
But Mr Alston says only an independent investigation will do.
"It is imperative, if the Kenya police are to be exonerated, for an independent team called from somewhere like Scotland Yard or the South African police to investigate," he said.
US ambassador to Kenya Michael Ranneberger said Washington was offering the services of the FBI to catch the perpetrators.
"The murders are a serious attack on human rights in Kenya," Mr Ranneberger said in a statement.
According to Mr Alston, the two human rights defenders were on their way to a meeting with a senior officer of the Kenya National Commission on Human Rights when they were shot at point-blank range whilst sitting in heavy traffic.
The killings have outraged the human rights community.
"The human rights community in Kenya holds the government fully and wholly responsible for the assassinations," Cyprian Nyamwamu of the Kenya Human Rights Consortium told the BBC's Network Africa programme.
Students react to the killings
"These two colleagues, members of the Oscar Foundation, are genuine, established, renowned human rights defenders," he said.
Mr Nyamwamu said there had been no attempt to save the men.
"The eyewitnesses on the scene saw the two vehicles create a jam, stop the traffic until they came out, gunned down these two human rights officers and paraded and ensured that nobody took these two to hospital until they were dead."
He said the police only arrived on the scene two hours later.
"This is just one kilometre away from the central police station in Nairobi. It's not in the bush," he said.
Mr Kingara's Oscar Foundation Free Legal Aid Clinic published a report last year, which said that 8,040 young Kenyans have been executed or tortured to death since 2002 in a police crackdown on a gang known as the Mungiki.
"It is a front so they can be able to carry out their activities," Alfred Mutua said.
Mainly drawn from President Mwai Kibaki's Kikuyu ethnic group, the Mungiki run transport rackets in the capital and are seen by some as a Kenyan version of the mafia.
Mr Mutua spoke as members of the sect led protests against police violence in the capital Nairobi and other towns.
They were calling for Mr Alston's recommendations to be implemented.
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