The family of Jermaine Baker, who was fatally shot during a police operation, have said those who knew and loved him "will keep him in their hearts and minds as they remember him".
They spoke as feelings continue to run high over the shooting of Mr Baker during an alleged attempt to spring two convicts from a prison van.
The 28-year-old, from Tottenham, north London, died from a single gunshot wound during the operation near Wood Green Crown Court last Friday.
The Independent Police Complaints Commission (IPCC) has said an officer has been arrested and interviewed under caution during its investigation into the incident.
Mr Baker's family issued a statement through Bhatt Murphy solicitors saying: "There has been a lot of speculation and misinformation in the media about Jermaine's background. There has also been considerable intrusion into our family homes and personal lives.
"As a family, we have found this insensitive and distressing. We would ask that in the future respect is shown to us and to Jermaine's memory.
"Those who knew and loved Jermaine will keep him in their hearts and minds as they remember him. Many of those people have already contacted us and shared their memories; we are grateful for their support and kind words.
"There has also been much speculation about the events leading to Jermaine's death. As his family we are of course anxious to find out the truth, and we look to the IPCC to carry out a full, thorough and prompt investigation. We would ask anyone with any information to contact the IPCC.
"At this time, we as a family are still processing the passing of a much loved son, father, brother, grandson, cousin, nephew, uncle, partner and friend. Please give us the time and privacy to grieve."
IPCC Commissioner Cindy Butts told a public meeting at Tottenham Town Hall on Thursday evening that an officer had been arrested and interviewed under caution.
The IPCC has launched a criminal homicide investigation into the death, which could see the police face murder or manslaughter charges. The officer was suspended from duty on Wednesday.
Ms Butts said: "The evidence we have at this stage does not mean that the officer definitively committed a criminal act and nor does it mean he will necessarily be charged with a criminal offence."
No relevant CCTV has been identified and no body-worn police cameras filmed the incident.
Ms Butts said the evidence was that Mr Baker was in a black Audi when he was shot.
She added: "In that car was what appears to be a non-police issue firearm. Further forensic examination will take place on the non-police issue firearm, and the firearm that was discharged by the police officer."
Chief Superintendent Victor Olisa, the Haringey borough commander, said there had been reports that Mr Baker was a gangster - but their research did not indicate that he was.
A close friend of Mr Baker told the meeting: "He was not a gangster whatsoever. I've been told that he was sleeping in his car. Police officers had information that was not 100% that he was going to do it - you took an innocent man away."
Ms Butts said: "We do not know whether he was or was not asleep."
Mr Olisa said later: "We are doing everything we can to listen to and understand the concerns raised by the local community.
"This is a very difficult time for everyone affected by the death of Jermaine. I am grateful that we can have this open meeting which provides a forum for people to air their strong views, which should be heard and understood.
"It is only by working together that we can move forward as a community."