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The Prime Minister has appealed for a calm response to the conclusions of the Mark Duggan inquest that found the 29-year-old was lawfully killed when shot by police in 2011.
David Cameron said he hoped people would respect the "proper judicial process" and welcomed the comments of Mr Duggan's aunt Carole, who said she wanted "no more violence".
Speaking to BBC London, Mr Cameron said: "We have to respect judicial processes in this country, we have to respect the outcome of trials and the work that juries do.
"I very much respect Mark Duggan's aunt for saying they want to pursue their case through the courts rather than on the streets, I think that's absolutely right.
"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."
He added: "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."
The police officer who was heckled as he attempted to make a statement following the Mark Duggan inquest has said the Metropolitan Police is at a "heightened" level of alert in case any violent disorder breaks out in response to the outcome.
Assistant Commissioner Mark Rowley was talked over by the enraged crowd who called out "murderer" and "murdering scum" as he tried to address the press outside the Royal Courts of Justice yesterday.
Speaking today, Mr Rowley said the strong reaction was understandable under the circumstances.
"I think anyone can understand a family who've lost a loved one," he said.
He added: "We don't have any information that there are people out there actively planning disorder but of course Londoners would think we were slightly naive if we had no preparation at all, so what we're doing today is what I would call a heightened state of readiness."
The "struggle" will go on for answers over the shooting of Mark Duggan but his aunt Carole insisted she wanted "no more demonstrations, no more violence".
Instead, she said the family would pursue the authorities through peaceful channels.
The Metropolitan Police commissioner has admitted the shooting has resulted in a "significant reduction in trust" between London's black communities and the police.
Sir Bernard Hogan-Howe will meet political representatives from London and local community leaders from Tottenham today to discuss how the police can build better relationships. He said he is "open to ideas and advice".
But Ms Duggan told BBC Radio 4's Today programme she was not yet ready to meet Sir Bernard and the family was still in "turmoil" about the case.
"The family are still in shock right now about the result of yesterday," she said. "We are in turmoil. We don't really know what's going to happen at this point. There will be something further down the line, I'm sure."
Latest ITV News reports
Met Police chief thanks Duggan family after they appeal for peace as friend says family are 'still too raw' to meet with police watchdog.
Jurors decided that he did have a gun but it was not in his hand when he was shot.