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Britain's top officer vowed to become an "implacable enemy" of racists at Scotland Yard as he agreed the force needed to "buck up its ideas".
Commissioner Bernard Hogan-Howe also said inquiries into 10 allegations of racism against the force would be finished within four weeks.
The police chief was confronted on LBC 97.3 radio by the brother of black bus driver Kester David, whose suspicious death in 2010 is to be reinvestigated by the force.
In a recording played to Mr Hogan-Howe, Roger David said: "I think your force needs to buck up its ideas and realise that black and ethnic people are here in Britain, we're part of society and we request and demand the same kind of treatments as white people in Britain...
"The police have to start from the top and go right down to the bottom and make sure that they get rid of, eliminate, any racial discrimination within the force."
Mr Hogan-Howe told radio host Nick Ferrari: "I agree with him. The first point I'd make is that this is the world's greatest diverse city and we're going to use that as a reason to be the best in the world at policing.
"We're not going to use it as an excuse for failing and sometimes I do hear us and sometimes others saying that the diversity of London means that we have a bigger challenge."
The force announced it would reinvestigate the death of Mr David, 53, almost two years after his charred remains were found under a railway arch.
Relatives campaigned for an independent inquiry after officers, who originally ruled out foul play, were accused of a catalogue of errors.
Ten other complaints of alleged racism - relating to 18 officers and one member of police staff - were referred to the police watchdog last week.
Mr Hogan-Howe said: "Racists will find me an implacable enemy. We will get rid of them, we will drive them out of the Met ...
"It is a serious issue and I think you can see that by the rigour and the vigour of what our response has been, that we're taking it seriously."
Mr Hogan-Howe said he launched the review of race allegations to ensure incidents do not go out of sight.
The force launched investigations after Pc Alex MacFarlane was temporarily stripped of his duties when a recording made of a suspect being called a "n*****" was made public.
The arrested man, named as Mauro Demetrio, 21, from Beckton, east London, was arrested on suspicion of drug driving but no action was later taken. He recorded the abuse on his mobile phone.
Mr Hogan-Howe said: "What happens when these investigations, if they go off to the IPCC and sometimes they go out of our sight, then we don't know the detail of the investigation, so the deputy commissioner said 'I want to know, are there any other cases, similar to the Newham ones, that we need to treat equally seriously?'.
"We found 10. So what I've said is, within the next four weeks, I want the investigations into those to be completed. So that is a major priority for the Met and then we'll get to the bottom. Are they true or are they false?"
PA