Mr Carmichael characterised the row as “scandal without the sex” and warned of the cosequences of the party “washing its dirty linen in public.”
His comments came as Lib Dem leader Nick Clegg insisted he would not back down over his demands that Lord Rennard should apologise to the four women who have made sexual misconduct allegations against the peer who is threatening to sue the party over his suspension on Monday.
But former Liberal leader Lord Steel called for Lord rennard to drop his legal threat and the party to reinstate him as a means to bring the dispute to an end.
Meanwhile one of the alleged victims Alison Smith, a former Aberdeen city councillor, called for the report into Lord Rennard’s behaviour by top QC Alistair Webster to be published.
She told BBC Radio 4’s Today programme: “As far as I understood, Lord Rennard has seen what I said. I haven’t seen the final report either and I would like to as much as the next person.”
Asked if it should be published, she replied: “Yes, actually I do, but actually I’ve appealed on the grounds that too much emphasis was placed on intent. I think the crux of the matter was whether he brought the party into disrepute, not whether he intended to behave as he did.”
Ms Smith said the women wanted the chance to tell Lord Rennard “what this is about”.
“If he’s not sure about intent, we want the chance to tell him exactly what this is about, exactly why power structures matter, exactly why it matters that he had the control of a woman’s career when he was making advances on people.”
Speaking on his LBC radio show Mr Clegg admitted that the scandal was “messy” but said there would be outrage if he had not demanded Lord Rennard apologise.
“Just imagine if we had done anything else,” he said.
“Just imagine if Alistair Webster (QC) had recommended that an apology should be issued and I came out and said ‘Thank you very much, we will file away the report, and by the way, none of the recommendations need to be accepted or adhered to’.
“There would have quite rightly been outrage.”
Calling for mediation behind closed doors, Mr Carmichael, a former Lib Dem chief whip who in the past had to resolve in ternal dispuutes, told a briefing of Scottish journalists in Westminster that the peer “should apologise”.
He said: “We are in a situation where youn have effectively got two camps and at a time when you are seeing the economy turning a corner, economic growth takling hold, I think there is a frustration amongst the party activisits that we are not able to talk about that because we are talking so much about our own internal matters.
“What I am quite keen to see is that there is a some sort of mediation set up that will allow both parties to find a way through this because clearly we have got something that now needs an early resolution and the only way I see achieving that is to have some third party involvement in mediation.”
He said mediation could be from a professional in the field or a party grandee but had to be “somebody trusted by both sides.”
He added: “We need to deal with it quickly and cleanly now.”
He said he had not decided who to back in the current election for deputy leader of the party but with Solihull MP Loreley Burt running to be the first woman to hold a UK leadership position he said that it needed to be “more reflective” of the electorate.