Lib Dem leadership contender Simon Hughes has said the way he has handled media pressure after admitting gay relationships is a mark of his courage.
He said it showed "he was not afraid of dealing with things" - a quality "which might be a leadership criterion".
The MP told Thursday's Sun he had had relationships with both women and men.
Asked about his recent denial when asked if he was gay, he said: "I gave a reply that wasn't untrue but was clearly misleading and I apologise."
The 54-year-old Lib Dem president said he had considered quitting the leadership race but had not come close to doing so.
He told BBC Radio Five Live the situation had become "unmanageable" this week as newspapers put more allegations, most of them untrue, to his campaign team.
The Bermondsey MP said he could not tell if the episode had damaged his leadership campaign.
He urged Lib Dem members to judge him on his experience, vision and campaigning.
"I hope they might think one other thing: that having gone through this experience and not disappeared, not backed away, that is a test and a sign that I'm not afraid of dealing with things that may be a criterion for leadership," he said.
Mr Hughes has slipped from odds-on favourite at the bookmakers to win the contest to 4/1 outsider.
His leadership rivals, Sir Menzies Campbell and Treasury spokesman Chris Huhne, both said his private life should not affect the leadership race.
Mr Hughes recently denied he was gay, saying he had "often" thought about getting married but had not been "as successful as I would have liked".
Asked by the Independent whether he was gay, he replied: "No, I'm not. But it absolutely should not matter if I was."
On Thursday, Mr Hughes said his reply had not been untrue, saying his relationships with both men and women meant he was not easy to "pigeon hole".
He said: "I apologise if I misled people, I apologise if I unintentionally gave the wrong impression.
"But I hope people will understand why people in public life try to put that sort of fence around them.
"And I hope they will understand that it shouldn't disbar people - not just me but anyone else - from public office or doing a job which I want to do and want to do well."
Mr Hughes was elected to Parliament in 1983 in a bitter by-election battle in Bermondsey against gay Labour candidate Peter Tatchell.
In one election leaflet, the Liberals presented him as the "straight choice" .
Mr Hughes said he had apologised publicly and privately for any part of the campaign which had been homophobic.
Gay rights activist Mr Tatchell said he had never considered "outing" Mr Hughes as he had not been hypocritical on gay issues.
"Although it is a pity Simon was, even recently, denying being gay, it is great that he has now come out," he said.
One Five Live listener, who said she was a Lib Dem member and a supporter of Mr Hughes who felt let down because he was trying to put "political spin" on the "non issue" of his sexuality.
Mr Hughes apologised, saying: "I hope you understand it is difficult to move from the position I took in 1980 to something else," he said.
Trevor Kavanagh, associate editor of The Sun, said Mr Hughes had decided to speak about his sexuality after being confronted with "pretty incontrovertible" evidence that he had phoned a gay chat line.
Mark Oaten earlier this month quit the Lib Dem front bench after his affair with a male prostitute was revealed. He had already pulled out of the leadership race saying he did not have enough support among MPs.