Ms Moroney told APNZ that once the true facts were given to Mrs Tolley, the minister should have come forward with that information.
While there was no obligation for a minister to correct information in Parliament if they subsequently found out what they had said was wrong, Ms Moroney said there was an ethical obligation to be honest with the public.
"Given the veracity of the minister's denial of the issue, there does need to now be a setting straight of the record from the Government's perspective."
She also criticised Mrs Tolley for putting out a press release accusing Ms Moroney and Radio New Zealand of broadcasting false information, and not retracting that once the facts were made clear.
She called on the Prime Minister to conduct a full inquiry into Mrs Tolley's handling of the issue.
However, Mr Key does not look likely to take the matter further, telling media this afternoon he had already spoken to Mrs Tolley.
"I'm satisfied with the answers she gave me, I think the ministry themselves have admitted that their processes weren't perfect," he said.
"The minister's confident she hasn't misled the House and that's the view of the Speaker, and I think that's right just on a quick, cursory reading of it."
Asked whether the minister should have made the correct information public when she received it, Mr Key said it "depends on the circumstances".
Mrs Mutu was stood down as principal at Te Kura Kaupapa Maori o Kaikohe in 2007 after her husband, John Hone Mutu, a teacher at the school, was suspended by the board of trustees.
Mr Mutu was suspended after an incident in 2004 when he visited a 15-year-old student at home, and was found lying on a mattress with her. Following the incident, Mrs Mutu ordered staff to tear up the student's written complaint.
The couple were struck off for serious misconduct and were each ordered to pay $20,000 in costs following a Teachers Council disciplinary tribunal hearing in October this year.
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-APNZ
