Rioters "should not take matters into their own hands and destroy their own communities", the father of murdered schoolboy Damilola Taylor has said.
Richard Taylor urged members of the public across London to "exercise restraint, patience and refrain from getting into violent activities".
"They should not forget that we are a community," he said.
"They should not take matters into their own hands and destroy their own communities.
"I urge community leaders to refrain from issuing inciting statements which will ignite more trouble.
"We all need to work together to address concerns and we give local authorities and the mayor a chance to deal with the situation at hand."
London Mayor Boris Johnson added that the scenes of violence and destruction were "utterly appalling".
"People have lost their homes, businesses and livelihoods through mindless violence," he said.
"I understand the need for urgent answers into the shooting incident that resulted in the death of a young local man, and I've sought reassurances that the IPCC (Independent Police Complaints Commission) are doing exactly that.
"But let's be clear - these acts of sheer criminality across London are nothing to do with this incident and must stop now."
Former England footballer Ian Wright, the mayor's mentoring champion, said: "I don't want young people to ruin their lives by getting involved in the opportunist violence we've seen this weekend.
"We know a lot of young people are disaffected and feel isolated, that's why I help push the mayor's mentoring scheme to try and turn around the lives of our young boys.
"Whatever frustrations you feel, destroying our communities is not the answer and it must stop now."
Shadow home secretary Yvette Cooper said: "For the second night there has been appalling violence and disorder on the streets of the capital, putting lives and public safety at risk. We condemn criminal violence utterly.
"Those involved in criminality should be brought to justice, gangs of looters should be stopped and arrested and we should all be supporting the police in these efforts.
"We also need calm but robust leadership and action in London now to prevent this disorder and criminality spreading to subsequent nights and continuing through the summer."
She went on: "Let's be clear, the Duggan family and communities in Tottenham and across London are not supporting this disorder.
"Immediate action is needed by the Government, the London mayor, the Met, local councils and communities all working together to address the violence and disorder, and prevent it extending for further nights."
The IPCC investigation was the right way to address concerns over the shooting of Mr Duggan, Ms Cooper said.
She went on: "A co-ordinated approach across London needs to draw a line and prevent disorder from spreading - this cannot be left to the already under-pressure police alone.
"We need to be assured that the police have the resources necessary to maintain public order but also to conduct targeted follow-up operations to bring criminals to justice.
"We also need a clear strategy from the government and the mayor to prevent this disorder becoming a repeated problem throughout August and September.
"That means looking swiftly at the capacity of the police and of prevention programmes, both of which are facing considerable resource pressure at the moment."