Clegg is coming under increasing strain over his leadership in the wake of the harassment allegations that have been levelled at the peer. Questions over his handling of the growing scandal are becoming louder with the added pressure of Thursday's Eastleigh by-election, called after the resignation of the disgraced former energy minister, Chris Huhne.
Cameron's backing of his deputy over the Rennard affair has been lukewarm
However, when asked if he had confidence in his deputy's handling of the affair, the PM wouldn't answer directly.
Cameron said: “Obviously these are serious issues and serious matters and they need to be taken seriously.
“The Liberal Democrats have set up two inquiries into this issue. I think you have to let those inquiries take place and make sure, as I’ve said before, they get to the bottom of these very important allegations.”
On Wednesday, Clegg conceded that his party had made "very serious mistakes" in failing to deal properly with complaints of sexual harassment against its former chief executive but again insisted that he was personally unaware of any specific allegations by women in the party until they were broadcast by Channel 4 last week.
But he suggested that the issue was "in the background" when the peer - who strenuously denies the alleged inappropriate behaviour - retired from his senior role on grounds of ill-health.
"There were some very serious mistakes and the women were not listened to and were let down," he said.
One of the women at the centre of the allegations said she would be going to the police on Thursday about allegations she is making about the peer's behaviour.
Alison Smith, a Lib Dem activist who is now a lecturer at Oxford University, told the BBC: "I will be talking to the police and I think the trial by media, probably it is time for that to finish."
She added: "I was told by Baroness Ros Scott that he had to leave because of his unacceptable behaviour, which I had raised with the party several times."
Ms Smith said the decided to "blow the whistle" because the peer had started to become involved again in a training event.
"We were told he was not going to make a comeback, now here he is, turning up all over the place," she added.
The deepening scandal has piled pressure on the Coalition party as it seeks to fend off the Conservative challenge in Eastleigh. Clegg's party is desperately fighting to hang on to the Hampshire seat to give a vital morale boost to the grassroots after support hit the doldrums on entering government.
Opinion polls suggest the race remains very tight but many observers are predicting the Lib Dems will hold off the Conservative challenge.