His comments were dismissed by Stephen's mother, Doreen, as patronising and she repeated her call for his immediate resignation.
There could be no way forward for Britain's largest police force while he was in charge, she said.
Giving evidence to the official inquiry into the death of Stephen, 18, Sir Paul admitted a number of his officers were racist.
Yet he repeatedly dismissed suggestions that the force was "institutionally" racist and denied that racism was responsible for the botched investigation into Stephen's death near his home in Eltham, south-east London. "I deeply regret that we have not brought Stephen's racist murderers to justice and I would like to personally apologise again today to Mr and Mrs Lawrence for our failure," he said.
"We have heard what people have been saying and I accept that a central concern is that the Met is racist. I acknowledge that we have not done enough to combat racist crime and harassment."
But he added: "If I believe that racism or corruption has impacted this case in any way, I would have already said so. I sincerely believe these issues did not influence this tragic case."
At times he was clearly embarrassed as he suffered persistent heckling from the Lawrence family supporters ("Condom, you're leaking") and tough questioning from the inquiry panel. On other occasions his performance bordered on farce as he struggled with phrases such as "identify the mischief" and "the challenge facing us" rather than refer directly to racism. Throughout the two hours and twenty minutes he spent at the inquiry it seemed that he was fighting to save his career.
Delivering his prepared speech, the Commissioner appeared reasonably at ease, outlining a series of reforms to counter racism within the police. He said the Deputy Assistant Commissioner, John Grieve, former head of the Anti-Terrorist Unit, had recently been appointed to head a new section dealing specifically with violent and racial crime.
But during the question-and-answer session he was less assured. He was repeatedly asked by the panel to admit the force was institutionally racist. Sir Paul refused to do so, denying that he was using "weasel words" but claiming that using such a label gave the wrong impression and would be harmful.
In one dramatic exchange, a panel member, Richard Stone, recalled South Africa's Truth and Reconciliation Commission and Bishop Desmond Tutu's offer to Winnie Mandela to confess her crimes. "Just say `Yes. I accept institutional racism exists'," he was urged. "I think a lot of people here are willing you to say that."
After a noticeable pause, Sir Paul countered: "The answer is that it would be very easy to please the panel and the [other] people here to say such a thing exists. I believe it would be dishonest for me to say that just to please you."
The panel also asked Sir Paul why he had informed the public as far back as 1993 that there had been no problems with the investigation when that was clearly not the case. The panel said Mr and Mrs Lawrence had found the attitude of officers investigating their son's murder, in April 1993, patronising.
Stephen's parents were clearly angered by the Commissioner's performance. Mrs Lawrence said: "Sir Paul has got fine words. I still have not been given the answer as to why Stephen's killers are still free.
"As I sat listening to Sir Paul this morning the word patronising came up in my head. I think it is just a PR job.
"For five years we have still not been given justice." She added: "I think he should resign and I think he should be asked to go."
She said she had met the mother of David Norris, one of the suspects, last weekend in Marks & Spencer in Bromley. "I cannot explain what I felt. It has taken me the whole weekend and I still have not got over the shock of it."
Stephen's father, Neville Lawrence, added: "I have been waiting patiently to hear Sir Paul Condon come here today and admit the wrongs that have been done to our family. It is now five years and families are still facing the things that we faced."
Lee Jasper, secretary of the National Assembly Against Racism, said: "Anti-racists and black communities are deeply disappointed by the evidence presented by Sir Paul Condon. It is not possible for the Met to make a few tinkering, cosmetic changes and expect that everything is business as usual."Reuse content