Jean Charles de Menezes' family has met officials investigating his killing by anti-terror police.
Jean Charles de Menezes' mother and father outside the IPCC
Relatives were shown CCTV footage of him at Stockwell Tube station, during a briefing at the Independent Police Complaints Commission in London.
Earlier, Metropolitan Police chief Sir Ian Blair said his offer to meet the Menezes family still stood.
He also called for a "broader consensus" on the police shoot-to-kill policy for suspected terrorists.
Mr Menezes, a 27-year-old electrician, was shot dead the day after the failed 21 July bombings in London.
Anti-terrorism police officers shot the Brazilian eight times at Stockwell station after mistaking him for a suicide bomber.
Members of his family who met Nick Hardwick, the IPCC chairman, included his mother Maria Otone de Menezes, his father Matozinhos Da Silva, his brother Giovani and his cousin Alex Pereira.
After the three-and-a-half-hour meeting, the family said it had agreed not to reveal details of what it was told so as not to prejudice any possible criminal proceedings.
But Giovani claimed that the CCTV footage proved that the police had "lied" when they said in the hours after the shooting that his brother had been acting suspiciously.
"The film showed that Jean did not have suspicious behaviour. For sure they lied to the family," he said.
Solicitor Harriet Wistrich added in a statement on the family's behalf: "We have many more questions to ask.
"This was the first of a series of meetings. We were shown the only available CCTV from Stockwell Tube.
"It was very distressing to see how completely relaxed and normal Jean Charles appeared, particularly in the light of statements made immediately after his death."
An IPCC spokesman said: "We will give the family as long as they need and as much information as we can."
Earlier, Sir Ian repeated his offer to meet the Menezes family.
He said: "I have offered to meet them. I am sorry at the moment they are saying that they won't."
Questioned by journalists before going into a meeting of the Metropolitan Police Authority (MPA), Sir Ian refused to speculate on the outcome of the IPCC's investigation.
"We will continue to work with the Independent Police Complaints Commission and wait for the outcome of that inquiry," he said.
He later told the MPA that the shooting of Mr Menezes was a "watershed moment".
He said it highlighted a need to "demonstrate democratic accountability" for the controversial policy of dealing with suspected terrorists.
But he said he was not sure what form the debate could take, because specific details about Operation Kratos - the policy which governs the use of firearms against suspects - could not be made public without threatening the police's effectiveness.
On Wednesday, Mr Menezes' family retraced his final journey from his south London flat to Stockwell.
The Menezes family arrived in Britain from Brazil on Monday and the trip has been paid for by Scotland Yard.