Stephen Lawrence was stabbed to death in 1993
The force continues to be heavily criticised for its investigation of the murder of the black teenager, stabbed to death in south-east London eight years ago.
Speaking on Radio 5 Live's Nicky Campbell programme, Sir John said he would do everything he could to ensure the culprits were brought before the courts.
But Duwayne Brooks, the friend of Stephen Lawrence who saw him murdered, confronted Sir John on air when he asked him why the police were wasting money on an inquiry where no-one would be charged.
Sir John Stevens was asked directly on the programme whether he knew who killed Stephen Lawrence.
Without hesitation he replied "yes".
Original suspects
Asked whether he was "100% sure", Sir John said: "We're pretty certain".
He did not say whether the people he believed were responsible were the five suspects originally identified by the police.
Three of them were later cleared, and under current law cannot stand trial for the crime again. But the case led for calls for the double jeopardy rule to be scrapped and plans for change were included in this year's Queens Speech.
It remains possible that the measure could be made retrospective.
'Waste of money'
Mr Brooks telephoned in to say it was a "waste of taxpayers' money" as no-one would ever be charged.
But Sir John said: "John Grieve, who is heading up the investigation, would
not pursue these avenues of inquiry unless he thought they were going to get a
result.
"We owe it to you and to the Lawrence family."
The Commissioner said that there are many cases coming before juries which, due to advances in forensics and other techniques, could not have been considered in previous years.
Sir John said every avenue was being explored to bring the killer to justice.
And he said police would never give up while there was hope that the killer could be put before the courts.
The Lawrence murder remains a thorny issue for Scotland Yard, with the Macpherson Report into it identifying "institutional racism" in the police.