Mr Menezes was fleeing officers when he was shot eight times
Tony Blair is reported to have called the President of Brazil to express his regrets for the mistaken killing of a man on the London Underground.
The office of President Luiz Inacio Lula da Silva said Mr Blair had given assurances that there would be an independent probe into the shooting.
Jean Charles de Menezes was shot eight times on a train after being mistaken for a suicide bomber on 22 July.
Number 10 refused to comment, saying Mr Blair's calls were "a private matter".
During their 10-minute conversation, Mr Blair told the president that Britain was "going through difficult times as a result of terrorist acts", the statement from the president's office said.
Meanwhile, Metropolitan Police Deputy Assistant Commissioner John Yates has travelled to the town of Gonzaga with Britain's ambassador to Brazil to meet the parents of 27-year-old Mr Menezes.
They are believed to have discussed the issue of compensation.
Deputy Assistant Commissioner Yates said he was "humbled" by the dignity shown by Mr Menezes' parents after the meeting at Gonzaga Town Hall.
"I'll carry back to London a very strong sense of the family's and the Brazilian people's powerful emotions at the regrettable death of an innocent man.
"I fully sympathize with this. We're deeply sorry."
British Ambassador Peter Collecott said in a statement: "Words will not bring Jean Charles back - but it is important for the family, especially for those living in Brazil, to know how deeply both the Metropolitan Police and the British government regret Jean Charles' death."
Mr Menezes' parents are expected to be offered financial help soon.
On Thursday the Home Office said the visa of Mr Menezes expired two years before he was shot by police.
A passport stamp apparently giving him indefinite leave to remain "was not in use" on that date, added officials.
A mass was held for Mr Menezes at Westminster Cathedral
But the Independent Police Complaints Commission (IPCC), which is overseeing the official investigation into the death, criticised the Home Office for releasing the information.
IPCC chairman Nick Hardwick said: "It's entirely irrelevant information. I'm rather surprised the Home Office should issue it."
"We won't be releasing partial information until we've independently established the facts."
Some of the dead man's relatives have questioned the police account of events and called for the banning of the Met's "shoot to kill" policy for suicide bombers.
Metropolitan Police chief Sir Ian Blair has apologised to Mr Menezes' family but defended the force's policy as the "only one way to stop someone who is a suicide bomber".