The man mistaken for a suicide bomber by police was shot eight times, an inquest into his death has heard.
Mr Menezes had been in London for more than three years
Brazilian Jean Charles de Menezes, 27, was shot seven times in the head and once in the shoulder, at Stockwell Tube station, south London, on Friday.
Det Insp Elizabeth Baker revealed the details at a hearing in London.
Security sources said Mr Menezes had an out-of-date visa, but his family denied this. Foreign Secretary Jack Straw said he believed he was legally in the UK.
Mr Menezes' cousin, Alex Pereira, who is based in London, said the police would "kill thousands of people" if they were not held accountable for what had happened at Stockwell.
He said: "They just kill the first person they see, that's what they did. They killed my cousin, they could kill anyone."
Brazilian media reports say British human rights lawyer Gareth Peirce is acting as the family's legal adviser, amid reports that they are considering suing Scotland Yard.
The Independent Police Complaints Commission (IPCC) will investigate the shooting.
Nick Hardwick, head of the IPCC, said the commission needs to find out the truth of what happened "to ensure it can never happen again".
He said that "if people haven't acted in accordance with the law and their training" they would be held accountable.
Mr Straw met Brazilian Foreign Minister Celso Amorim in London, where they discussed the return of Mr Menezes' body to Brazil.
Both Mr Straw and Mr Amorim said they believed he was living in the UK legally - though there are reports that his precise immigration status is still being checked.
"I haven't got any precise information on his immigration status, my understanding is he was here lawfully," Mr Straw said.
The Home Office could not confirm his immigration status but said they were looking into it "as a matter of urgency".
Meanwhile, detectives are still hunting for the men who attempted to blow up three London Tube trains and a bus last Thursday.
A total of five people have been arrested in connection with the attempted bombings and the police have named two suspects: Muktar Said-Ibrahim, 27, also known as Muktar Mohammed-Said, and Yasin Hassan Omar, 24.
Tony Blair said he was "desperately sorry" an innocent man had lost his life.
The prime minister said it was right for Britain to express its "sorrow and deep sympathy" to Mr Menezes' family.
But he said the police must be supported in doing their job.
He added that they would have been criticised had the suspect turned out to be a terrorist and they had failed to take action.
Mr Menezes' cousin says the police "must pay"
London Mayor Ken Livingstone described Mr Menezes as a "victim of the terrorist attacks".
He said: "Consider the choice that faced police officers at Stockwell last Friday - and be glad you did not have to take it."
On Friday morning, Mr Menezes had left his flat in Tulse Hill and boarded a bus towards Stockwell Tube station.
He had been followed by police, who had his block of flats under surveillance.
When he was challenged by police in the Tube station, he fled, reportedly leaping the ticket barrier.
Over the past year there have been an increased number of immigration checks at Tube stations - a policy widely reported in Brazilian papers in London.
Police chased him on to a Tube train where he was shot dead.
In Brazil, relatives are demanding answers as to why Mr Menezes ran and why he was shot by police.
Cousin Maria do Socorro, speaking before his immigration status had been questioned, said she thought the police had acted "like amateurs".
She told BBC Radio 4's Today programme: "If you are going to have a war on terror, you have got to use brains to fight it not just brute force."
Ms Socorro said the family were considering suing over the shooting.
Friends of Mr Menezes in London said he had recently returned to Brazil for eight months to be with his father, who was being treated for cancer.
Fausto Soares, 26, said Mr Menezes had been sending money to pay for the treatment and was concerned how the family would now cope financially.
BBC home affairs correspondent Danny Shaw said the type of visa Mr Menezes had been given would normally be valid for one-and-a-half to two years.
He said Mr Menezes had not renewed the visa, adding: "That wouldn't explain why he was shot, but it might provide an explanation as to why he ran away - if that is indeed what he did do."