But Sir Ian Blair has strongly defended his actions and those of his officers in the aftermath of the shooting.
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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.
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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.
http://news.bbc.co.uk/2/hi/uk_news/4164856.stm