In an interview after the high-profile trial over the killing of the black teenager, who was attacked by a racist gang in 1993, Mr Cameron said the UK was a "less racist country" than at the time of Stephen's death.
But he said people from minority ethnic backgrounds still faced disadvantage.
Asked about the future of the Metropolitan Police's Lawrence inquiry team on Sky News's Boulton and Co show, Mr Cameron declined to comment.
"It's a matter for the police," he said. "They must feel empowered to seek the truth and find justice.
"The Metropolitan Police and Metropolitan Police Authority – I believe in trusting them to make those decisions and I think it is right that they should."Asked whether race relations had improved since 1993, Mr Cameron said: "I think we are a less racist country but we have still got a problem with racism.
"We have still got a problem of people from different racial backgrounds being disadvantaged in Britain.
"I think the country has come a huge way since that dreadful murder, but there is still a lot more to be done."
His comments came after the only witness to Stephen's killing described how he had been victimised in the 18-year wait for justice.
Duwayne Brooks told BBC Radio 4's Today programme: "For 18 years, I have endured harassment, victimisation, being blamed for the first prosecution failing, being brutalised and having false charges brought against me.
"To see two members of that gang being convicted – for me it was all worth it.
Stephen Lawrence's father says he has been able to dance for the first time in nearly 19 years since the murder of his son.
Neville Lawrence, reportedly an accomplished jazz, soul and blues dancer, said he had pledged never to dance again until somebody was "doing time" for the 1993 murder of his son.
He told ITV Daybreak that the convictions last week of Gary Dobson, 36, and David Norris, 35, for the murder of 18-year-old Stephen had been a "watershed" moment for him.
"It is like you are underwater and holding your breath - when the verdict was read out, 'guilty', I could not even believe it, because we had been waiting for so long, it is almost 19 years," he said.
"Tears just started to roll out of my eyes - the relief.
"One of the things which I have done over the years is to make a promise to myself that I would never dance again until somebody was doing time for the murder of my son.
"This weekend I was able to dance for the first time in 18 years."
By Donna Bowater taken from http://www.telegraph.co.uk/news/uknews/law-and-order/9002758/David-Cameron-Britain-still-has-a-problem-with-racism.html