Tom Watson has said it was his "duty" to notify the Director of Public Prosecutions about allegations made against Leon Brittan.
Lord Brittan's brother, Sir Samuel Brittan, has said the deputy leader of the Labour party should apologise after police dropped a rape inquiry against the former home secretary who died earlier this year.
But writing on the Huffington Post website, Mr Watson outlines his belief that he acted appropriately.
He writes: "As the tributes flowed in from his lifelong friends I felt for those people who claimed he abused them.
"I repeated a line used by one of the alleged survivors, who said: 'He is close to evil as any human being could get.' I shouldn't have repeated such an emotive phrase.
"The choice facing anyone who is presented with testimony of this kind is whether to pass it on to the authorities and urge them to investigate or to ignore it.
"I chose the first option. I felt it was my duty to do so."
In the piece for the Huffington Post, Mr Watson writes that he contacted the DPP in 2014 because he felt the allegations he had been made aware of against Lord Brittan "should be fully investigated".
Mr Watson does state that he is sorry for the "distress Leon Brittan's family experienced as they grieved for him" as a result of the claims.
He also outlines his belief that Lord Brittan "would have been interviewed even if I hadn't intervened because the DPP made it clear in her reply to my letter that the police investigation into him was ongoing".
Sir Samuel has accused Mr Watson of making "unfounded accusations" which prompted police to reopen the case against Lord Brittan.
It comes after the Times reported Scotland Yard deputy assistant commissioner Steve Rodhouse had written to Lord Brittan's widow to apologise for failing to tell the family the peer had been cleared before his death.
Lord Brittan died of cancer earlier this year, unaware that police had decided there was no case for him to answer over allegations that he raped a 19-year-old student in 1967.
Journalist Sir Samuel told the Daily Mail: "He should apologise to my sister-in-law for making unfounded accusations against my brother. And he should apologise in public as well."
The Crown Prosecution Service found in July 2013 that there was not enough evidence for a prosecution, but the decision was never passed on to the peer.
The case was reopened last year after Mr Watson wrote to the Director of Public Prosecutions and Lord Brittan was interviewed under caution, when he was seriously ill.
Scotland Yard said: "The Metropolitan Police Service is preparing a detailed response to the mayor of London's request for an explanation in the delay in informing the widow of a man in his 70s investigated for rape that there was insufficient evidence to proceed to a charge.
"The MPS expects this response will be given to him next week, once all the material has been reviewed."