They accused Met Police chief Sir Ian Blair of lying about aspects of the shooting, and of attempting a cover-up.
Sir Ian has "rejected utterly" the claims and said some of the disputed statements were never provided by his force. He has said he will not resign.
Mr Menezes was mistakenly shot as a suspected suicide bomber on 22 July.
Brazilian investigators are to fly to London next week for talks with the Independent Police Complaints Commission (IPCC) to clarify conflicting reports of how he died at Stockwell station.
The incident came a day after the failed 21 July attacks on the London Underground and a bus.
Investigation papers leaked to the media this week seemed to contradict initial police statements and eyewitness accounts of events.
And the IPCC has said Scotland Yard "initially resisted" the regulator's attempts to launch an investigation into the shooting.
Mr Menezes' cousin Alessandro Pereira said: "For three weeks we have had to listen to lie after lie about Jean and how he was killed."
Speaking at a press conference near Stockwell station, Mr Pereira said: "I want Ian Blair to think how it felt having to ring Jean's mother and father... and tell them their son was dead, that he was killed in such a way.
"The police know Jean was innocent and yet they let my family suffer."
He said lies had been told about his cousin such as that he was a suspected terrorist, that he looked like a suicide bomber, that he was wearing a big jacket and that he ran from police.
But Sir Ian Blair has strongly defended his actions and those of his officers in the aftermath of the shooting.
In an interview with the London Evening Standard on Thursday, Sir Ian said people had to be careful about attributing statements to the police.
"We have looked at what we have actually said about this incident. The number of features about heavyweight coats or hopping over barriers have never been said or confirmed by the Metropolitan Police Service.
"I did say there were direct links to the investigation and that is because he [Mr Menezes] came out of the house that we had under surveillance."
The BBC's home affairs correspondent Daniel Sandford said he did not think Sir Ian's position was at risk, but he would have to "sit it out" and take the criticisms.
He said it was important to note where the calls for Sir Ian's resignation were not coming from - and pointed out that no such call had come from the government, London Mayor Ken Livingstone or his employer the Metropolitan Police Authority.
Yasmin Khan, from the Jean Charles de Menezes' Family Campaign, said the family had witnessed a "Laurel and Hardy police operation" in recent weeks.
She said there were three issues to consider, the first being the "shoot-to-kill policy", and the second the "incompetence of the police on the day".
"Thirdly the attempted cover-up and misleading by Ian Blair, the Metropolitan Police and with government officials colluding with this," she said.
She urged supporters to attend a vigil to be held outside 10 Downing Street at 1800 BST (1700 GMT) on Monday.
Chair of the Metropolitan Police Authority (MPA), Len Duvall, said Mr Menezes' death was a "tragic loss" but added the officers involved would also be under "immense strain" and needed support.
"The MPA will do everything in its power to ensure that whatever the circumstances surrounding the fatal shooting of Mr de Menezes, the full facts and truth will be made known," he said.
Mr Duvall added London was facing an "unprecedented" potential threat to the safety of its inhabitants.
"This means calculated risks have to be taken, often by necessity in haste, and mistakes are therefore likely," he said.
Graphic photos of Mr Menezes' dead body lying on the floor of the Tube train have appeared in most of Brazil's newspapers.
The papers also reported claims from the leaked documents that the Brazilian electrician had not fled from police as initially claimed, nor had he hurdled a ticket barrier.
The Brazilian Foreign Ministry said the press coverage had heightened the government's sense of indignation at the shooting.