Labour's Maori development spokesperson Nanaia Mahuta said if the minister did not have confidence in the board, they needed to go.
"She should stop stalling and demand their resignations," Ms Mahuta said.
"As long as the Minister fiddles, nothing will change. Too much is at stake and decisive action is required."
Ms Mahuta said Ms Parata knew about the problems facing the board and its management when former board member Toni Waho gave her the information, and should have acted then.
She said with the appointment of a new chief executive, there was the opportunity to create change if the minister acted now.
In response, Ms Parata said it wasn't for her to say whether she had confidence in the board.
"I don't appoint the board and it doesn't answer to me. It answers, or should answer, to k?hanga wh?nau," she said.
The minister said the board told her in February it was planning a new governance process. She said the board should put in place a governance entity that "meets the modern tests of representativeness, transparency, accountability, and auditability".
She said she had acted when Mr Waho alerted her to concerns about the board, by referring allegations to the SFO.
Meanwhile, King Tuheitia's office has refused to answer questions about the $110,000 paid in directors fees to the King when he was not a director.
A person at the Kingitanga office told the Herald: "No one is going to talk to you sweetheart. There is no comment."
Te Kohanga Reo Trust Board spokesman Derek Fox said the fee was legitimate, but had been written up wrong - it should have been labelled a honorarium.
King Tuheitia was the patron of the trust and because of that the trust wanted to pay him an honorarium - he hadn't asked for it.
"It's not necessarily for him, it's for the kingitanga," Mr Fox said. "He, and his mother before him do a lot for Kohanga Reo."
Native Affairs reported the issue had been handed to the Inland Revenue Department. IRD refused to discuss the case.
The story which ran last night was one of the episodes that reportedly cost Maori Television its star broadcaster.
Executive interference in the Kohanga Reo story, and another on Whanau Ora, was believed to be a factor in Mihingarangi Forbes' resignation from Native Affairs earlier this month.
The piece focused on misspending at the Te Kohanga Reo National Trust Board and its wholly-owned subsidiary Te Pataka Ohanga Limited, a follow up to an earlier investigation by the show.
The previous investigation won the Best Investigative Reporting award at the 2014 World Indigenous Journalism Awards with judges saying it was "an excellent example of the rigour with which we need to conduct ourselves as journalists."
New information in the show including the review of Te Pataka Ohanga and the Te Kohanga Reo National Trust by Internal Affairs, which found further financial issues.
It said Te Pataka Ohanga paid themselves bonuses including koha not approved by the board, and used credit cards to purchase personal items.
Board members had also been allowed to take personal loans.
Ousted board member Toni Waho, who spoke exclusively to the programme, said he had one of the loans, which he now agreed was "not a good look".
Mr Fox said today that since then Te Pataka Ohanga had cancelled credit cards and suspended personal loans, among other measures to ensure financial accountability.
Native Affairs reported Te Pataka Ohanga was now on an Inland Revenue watch list, and had been given a formal warning.
The show also revealed the trust had made two payments totaling $800,000 for termination fees in 2007.
The trust appointed a new chief executive last month, a former Ministry of Education official named Kararaina Cribb.
Mihingarangi Forbes will now begin a new role with Radio New Zealand.
Internal Affairs report into Te Pataka Ohanga
Internal Affairs report into Te Kohanga Reo National Trust Board
