Police should have clarified misleading reports about the shooting of Jean Charles de Menezes, a member of the Metropolitan Police Authority has said.
Mr Menezes was shot a day after the failed London bombings
Leaked investigation papers seemed to contradict initial police statements and witness accounts of the shooting.
Green authority member Jenny Jones said it should have been "an immediate priority" for police to clarify the information after the 22 July shooting.
Meanwhile, police say there has been no compensation offer to the man's family.
Some reports said $1 million (£560,000) had been offered, but the Met police said: "The only discussions we have had so far with the family of Jean Charles de Menezes have been about initial expenses, and we strongly refute any suggestion that a figure anywhere in the region of $1 million has been offered as compensation."
Scotland Yard was quoted as saying that Mr Menezes' "clothing and demeanour" added to suspicions that he was a suspected suicide bomber.
However, the leaked documents and photographs show the body of Mr Menezes, on the Tube where he was shot dead by police, wearing a denim jacket - not a bulky one as previously described.
Ms Jones said: "My concern is that even if the leaks didn't come from the police... they should have cleared it up.
"It should have been an immediate priority to put out some sort of acknowledgement that these were false and malicious rumours.
"They didn't do that and that is something they have to look into," she told BBC News 24 on Saturday.
The MPA is an independent authority that scrutinises the work of the London police force.
Brazilian investigators are to fly to London next week for talks with the Independent Police Complaints Commission to clarify the conflicting reports.
Metropolitan Police chief Sir Ian Blair urged the public not to let the shooting overshadow the deaths of 52 victims of the London bombers.
He told BBC Radio 4 that the police took responsibility for the Brazilian man's death and had apologised.
But he said: "We can't let that one tragic death outweigh all others."
Mr Menezes' family has called for Sir Ian to resign, and accused him of lying about aspects of the shooting and of attempting a cover-up.
The incident came a day after the failed 21 July attacks on the London Underground and a bus.
And the IPCC has said Scotland Yard "initially resisted" the regulator's attempts to launch an investigation into the shooting.
In an interview on Radio 4's Talking Politics show - broadcast on Saturday - Sir Ian rejected the allegations.
"The thing that I would want to say is that of all the allegations made in the last couple of days, the matter I would most want to reject is the concept of a cover-up.
"If one was going to cover something up, you wouldn't cover it up by writing a letter delivered by hand to the permanent secretary at the Home Office, the chairman of the Metropolitan Police Authority and the chairman of the Independent Police Complaints Commission itself."
Sir Ian called for Mr Menezes' death to be put in context.
"Tragic as the death of Mr Menezes is, and we have apologised for it and we take responsibility for it, it is one death out of 57.
"The context here is the largest criminal inquiry in English history with 52 innocent victims dead, still double figures of people whose lives have been wrecked, four dead bombers and we can't let that one tragic death outweigh all others."
The full interview was broadcast at 1100BST on Radio 4's Talking Politics programme