Metropolitan Police Commissioner Sir Paul Stephenson acknowledged that mistakes in the case had resulted in "profound consequences".
Baroness Scotland said she had invited the Metropolitan Police Commissioner, Sir Paul Stephenson, to begin an inquiry.
Sir Paul Stephenson stood down amid the phone-hacking scandal and applications to be his successor close on Wednesday.
Metropolitan Police Commissioner Sir Paul Stephenson has also called for an end to all bonuses for police officers.
The other men under investigation include Commissioner Sir Paul Stephenson and Assistant Commissioner John Yates, who both quit this week.
Commissioner Sir Paul Stephenson said he was "very saddened" by the deaths.
Metropolitan Police Commissioner Sir Paul Stephenson ordered an internal review into the incident, which has been presented to Home Secretary Theresa May.
His appointment as Commissioner in September 2011 followed a period as Acting Commissioner in the period after his predecessor Sir Paul Stephenson's resignation.
Metropolitan Police Commissioner Sir Paul Stephenson has resigned, having faced criticism for hiring former News of the World executive Neil Wallis as an adviser.
BBC: Hacking: Miliband and Clegg seek media ownership limits
Sir Paul Stephenson, Britain's most senior police officer, resigned on Sunday after facing criticism for the Met's recruitment of Mr Wallis as a PR consultant.
Later that day, Sir Paul Stephenson, the commissioner of the Metropolitan Police, and thus the senior law-enforcement official in the land, also quit his job.
We are being told that Britain's top policeman, Sir Paul Stephenson, has resigned in order to take responsibility for the failures in the Metropolitan Police.
Writing on his blog, Peter Fahy said he had no wish to replace the outgoing commissioner, Sir Paul Stephenson, who quit over the phone-hacking scandal.
BBC: Peter Fahy rules himself out of Met commissioner contest
The independent Mayor of Middlesbrough, Ray Mallon, said he had also written to the Metropolitan Police Commissioner, Sir Paul Stephenson, asking him to investigate the revelations.
First to go was the commissioner himself, Sir Paul Stephenson.
The force's acting commissioner, Tim Godwin - standing in for Sir Paul Stephenson while he recovers from an operation - met committee chairman Keith Vaz on Wednesday to apologise for the false evidence.
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