The Guardian newspaper reported that a former undercover officer had told them he was part of an operation to spy on relatives of teenager Stephen Lawrence, who was stabbed to death at a London bus stop on April 22, 1993.
"The Prime Minister is deeply concerned by reports that the police wanted to smear Stephen Lawrence's family and would like the Metropolitan police to investigate immediately," a spokesman for Cameron said.
The killing of 18-year-old Stephen Lawrence sparked an overhaul of British policing after an official report found that "institutional racism" had tainted the original investigation.
But in the new claims, the Guardian quoted undercover cop Peter Francis as saying that he had posed as an anti-racist activist in order to try and obtain information which would discredit the campaign for a more thorough investigation.
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"I had to get any information on what was happening in the Stephen Lawrence campaign," Francis told the paper.
"Throughout my deployment there was almost constant pressure on me personally to find out anything I could that would discredit these campaigns."
Two white men, Gary Dobson and David Norris, were convicted of the murder in January 2012 on the basis of new forensic evidence. They lost an appeal against their life sentences in August.
They were among five suspects arrested within days of Lawrence's murder, and police say that the investigation into possible accomplices remains "live".
Lawrence's mother, Doreen, told the paper that there was no justification in "trying to discredit the family and people around us.