Mr Little said these new details showed Mr Rennie was "unfit for the job".
"The information that ... he was advised by an experienced, in-house communications adviser not to run a media conference, which has always been the issue, takes it beyond a lapse of judgment into a woeful lack of judgment."
State Services Minister Paula Bennett reiterated her confidence in Mr Rennie, though she was unhappy with his handling of Mr Sutton's resignation.
"[Mr Rennie] accepts that it should have been handled differently ... More importantly, he has expressed his regret at any hurt his actions last Monday may have caused the woman who has come forward."
Mr Rennie said yesterday he had a number of advisors who gave him free and frank advice.
"I am confident this is what I received in this case. Responsibility for all decisions rests with me," he said.
The decision to allow Mr Sutton to speak at the press conference has been widely criticised, in particular because he and the complainant were bound by a confidentiality agreement. It was also attended by several high-level officials, giving an impression of support for him.
Equal Opportunities Commissioner Jackie Blue said the handling of the investigation could have a "chilling effect" on victims of alleged sexual harassment speaking out.
Cera staff battle on
Staff at the Canterbury Earthquake Recovery Authority are trying to keep the region's rebuild on track despite the "surreal" situation they find themselves in.
Throughout the public furore surrounding former chief executive Roger Sutton's resignation after allegations of sexual harassment, Cera workers have tried to continue with "business as usual".
But sources say the mood inside the public service department charged with co-ordinating the post-quake rebuild is "mixed".
"Some people are still in support of [Sutton]," said one insider. "Some are glad he's resigned, others are shell-shocked, and others are just keeping their heads down."
Mr Sutton had intended to continue in his $500,000-a-year job until January 31, but on Wednesday it was announced he would stand down, replaced by acting CEO John Ombler.
It is understood Mr Sutton circulated an internal email on Wednesday in which he expressed his pride in the work of staff since the February 22, 2011, earthquake.
- NZME.