The Prime Minister has called for calm after an inquest jury found that Mark Duggan was lawfully killed by a police marksman.
David Cameron expressed his sympathy and praised the family’s decision to pursue the case legally “rather than on the streets”.
Mr Duggan, whom police claimed was involved in the Tottenham Man Dem gang, was killed by armed police who pulled over the minicab he was driving in as part of a gun crime operation.
Speaking on BBC Radio London, Mr Cameron said: "Of course these issues raise very strong emotions.
“But I hope people can react calmly and recognise that we have proper judicial processes in this country and they are the ones that must be followed and respected."
Meetings were held in Tottenham today between community leaders and the Metropolitan Police in an attempt to rebuild trust with the community.
But Mr Duggan’s family have declined to attend a meeting the Sir Bernard Hogan-Howe, the Met’s commissioner.
The Prime Minister said: “I very much respect Mark Duggan's aunt for saying they want to pursue their case legally, rather than on the streets. I think that's absolutely right.”
He added: “I have huge respect for Bernard Hogan-Howe who I know is ready to meet with the family if they would like and recognises how much more important work we still have to do to make sure the police have the confidence of every community in London.”
Mr Cameron also recognised that racial prejudice was still an issue across the country.
“There is still racial prejudice in our country, there is still discrimination.
“But I think what you can see is governments of all colours, whether Labour or Conservative, have been trying to break down these barriers and trying to end discrimination and trying to make sure that people are valued for the passion in their hearts and the thoughts in their head rather than the colour of their skin or their sexuality.”