Met Police Assistant Commissioner John Yates has quit after growing pressure amid the phone-hacking scandal.
Mr Yates checked the credentials of Neil Wallis before the Met employed the former News of the World executive, arrested last week over hacking claims.
He said his conscience was clear and had "deep regret" over his resignation.
Meanwhile, the Independent Police Complaints Commission has received referrals about the conduct of four current or former senior Met officers.
Mr Yates said in a statement: "Sadly, there continues to be a huge amount of inaccurate, ill-informed and on occasion downright malicious gossip published about me personally.
"This has the potential to be a significant distraction in my current role as the national lead for counter terrorism.
"I see no prospect of this improving in the coming weeks and months as we approach one of the most important events in the history of the Metropolitan Police Service, the 2012 Olympic Games.
"The threats that we face in the modern world are such that I would never forgive myself if I was unable to give total commitment to the task of protecting London and the country during this period. I simply cannot let this situation continue."
The IPCC said four referrals relating to the police's phone-hacking investigation involved Commissioner Sir Paul Stephenson, who resigned on Sunday, and Mr Yates, as well as two other former senior officers. The BBC understands the other two officers are former Assistant Commissioner Andy Hayman and former Deputy Assistant Commissioner Peter Clarke.
A fifth referral relates to the alleged involvement of Mr Yates in inappropriately securing a job at the Met for the daughter of a friend. The BBC understands the woman to be Amy Wallis, daughter of Neil, and that she works in a civilian non-operational role.
The referrals come from the Metropolitan Police Authority (MPA).
In other developments on Monday:
- undefined for hiring former News of the World editor Andy Coulson at Number 10
- Former News International chief executive Rebekah Brooks confirmed she would appear before a committee of MPs on Tuesday, alongside Rupert and James Murdoch, despite her arrest and questioning by police on Sunday
- News Corporation established an independent body headed by senior barrister Lord Grabiner QC to lead its internal inquiry into the News of the World phone-hacking scandal
- Shares in News Corporation dropped by 7.6% to a two-year low in trading in Australia, and suffered a 4.3% fall in New York
- The Serious Fraud Office said it would give "full consideration" to a request by Labour MP Tom Watson to investigate out-of-court settlements made to hacking victims
- Press Association reporter Laura Elston will face no further action, her lawyer said . She had been arrested last month by police investigating allegations of phone hacking by journalists
Sir Paul, the most senior policeman in Britain, resigned after facing criticism for the force's recruitment of Mr Wallis as a PR consultant.
Mayor of London Boris Johnson said Deputy Commissioner Tim Godwin would be in charge at Scotland Yard until Sir Paul's replacement was appointed. Mr Yates will be replaced in the interim as the Met's head of counter-terrorism by Assistant Commissioner Cressida Dick.
Mr Johnson said it was right for both Sir Paul and Mr Yates to stand down.
He told a news conference at City Hall in London: "There is absolutely nothing that has been proven against the probity or the professionalism of either man.
"But in both cases we have to recognise that the nexus of questions about the relationship between the Met and the News of the World was likely to be distracting to both officers in the run-up to the Olympic Games."
Home Secretary Theresa May said in a statement to MPs that she was "sorry" over Sir Paul's decision to resign and that the Met was "stronger operationally today than it was when he took over".
She added: "I want to put on the record my gratitude to John Yates for the work he has done while I've been home secretary to develop and improve counter-terrorism policing in London and indeed across the whole country."
Ms May announced that HM Inspectorate of Constabulary would launch an inquiry into corruption in the police, and Independent Police Complaints Commission investigations on the same issue would be part of the judge-led inquiry into the hacking scandal.
Mr Cameron, who is on a trade visit to Africa, said: "John Yates was a well-respected detective, and has more recently provided strong leadership on counter-terrorism policing. What matters now is that we ensure swift and effective continuity at the Metropolitan Police Service."
The prime minister is cutting short his trip to prepare for a statement to the Commons on Wednesday. He earlier announced the recall of the Commons to debate the latest developments in the phone-hacking scandal.
Mr Wallis, a former NoW deputy editor, was arrested and released on bail on Thursday on suspicion of conspiring to intercept communications.
The day after the commissioner's resignation, Mr Yates told Metropolitan Police Authority (MPA) chairman Kit Malthouse that he was also standing down.
Scotland Yard said in a statement: "Assistant Commissioner John Yates has this afternoon indicated his intention to resign to the chair of the MPA. This has been accepted."
Mr Yates's resignation came after he was informed he would be suspended pending an inquiry into his relationship with Mr Wallis.
The officer had been confronted with new information about the friendship between the two men, sources told BBC political editor Nick Robinson.
After a meeting of the Metropolitan Police Authority's professional standards committee, the MPA said in a statement: "The committee considered allegations concerning Assistant Commissioner John Yates and after lengthy and careful deliberations decided to suspend the assistant commissioner.
"Suspension is not a disciplinary sanction and it is emphasised that suspension should not be taken as a presumption of guilt. Assistant Commissioner Yates has been informed of this decision.
"A number of matters have been referred to the Independent Police Complaints Commission, including one involving Assistant Commissioner Yates."