Bernard Hogan-Howe 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.
More top news
A school with fees of £8,000 a term has been criticised for including a lunch of baked potatoes in an "austerity day".
The family of notorious murdered criminal John "Goldfinger" Palmer have offered a £100,000 reward.
More than 2,000 people gathered at Westminster Abbey to celebrate the 70th anniversary of the arrival of the Windrush generation.