Metropolitan Police chief Sir Ian Blair has the prime minister's full backing, Downing Street has said.
Mr Menezes' family have called for Sir Ian to resign
When asked if Tony Blair had full confidence in Sir Ian over his handling of the Jean Charles de Menezes case, a spokeswoman said: "Yes."
Mr Menezes' family want Sir Ian to resign for wrongly linking the shooting to the attempted bombings early on.
Sir Ian has told the News of the World it was 24 hours before he learned the Brazilian was wrongly shot dead.
The family's lawyer expressed "incredulity" that he made statements without knowing facts.
Deputy Prime Minister John Prescott, who is currently in charge of the government while the prime minister is on holiday, also endorsed Sir Ian, telling BBC News the police chief had his support.
When asked if the police commissioner had his "full and unqualified confidence", Mr Prescott replied: "Yes".
Mr Menezes, a Brazilian electrician, was shot by police at Stockwell tube station on 22 July - the day after several failed bomb attempts - when he was mistaken for one of the bombing suspects.
Later the same day Sir Ian said the shooting was "directly linked to the ongoing and expanding anti-terrorist operation".
Scotland Yard has confirmed that an offer of £15,000 has been made to the Menezes family in addition to any funeral costs or travel expenses.
It stressed that it was intended to be an "ex gratia" payment, which would not affect any further compensation or legal action.
But the family rejected the offer, which is said to have caused them offence.
Scotland Yard has been criticised because the offer was made in a complex legal letter written in English to the family, who only speak Portuguese.
Mr Prescott said he had not seen the letter but it would be "terrible" if the reports were true.
He said: "I haven't seen the letter and I think it would be terrible if it was done that way.
"It does sound not a very sensitive way to deal with such a difficult matter."
Gareth Peirce, whose firm Birnberg Peirce is representing the Menezes family, described the approach by the Met as "disturbing".
It might have been a "deliberate attempt to ensnare families into inappropriate agreements or inappropriate decisions", she said.
"There was a complete failure either to inform lawyers who were acting for the family that they were going and a complete failure as a courtesy to tell the family they were going."
The family earlier accused police of not doing enough to stop misleading speculation about the shooting in the days after the attacks.
Sir Ian has said the shooting had to be put into context
Leaked documents from the police investigation into the death appeared to contradict initial police and witness statements about the incident.
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.
But former Scotland Yard commander Roy Ramm has defended Sir Ian, telling BBC Radio 5 Live: "What Blair said - and he prefaced all his remarks with 'as far as I know', 'as I understand it' - was what he understood to be the truth at the time.
"It does not surprise me it took a full 24 hours to look at all that information and realise they had it wrong."
The family, from the Brazilian town of Gonzaga, showed the letter offering the money to journalists on Saturday, denying media reports that £500,000 had been offered.
In an interview on Radio 4's Talking Politics show on Saturday Sir Ian said the shooting had to be put into 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."
Brazilian investigators are to land in London on Monday for talks with the Independent Police Complaints Commission to clarify the conflicting reports.