The Māori Language Commission says a $200,000 cap on the chief executive salary is hampering its ability to find someone with the right skills for the role.
But the Māori Development Minister isn't interested in getting involved.
The Māori Language Commission has been without a permanent leader for more than a year.
At the moment, the job is being done temporarily by academic Dr Poia Rewi.
The commission said it was keen to fill the vacancy, but the pool of potential applicants was small.
In a briefing to MPs, it pointed out the salary could be a hindrance, noting a cap of $200,000 inhibited hiring people with the right skills.
It said it had not yet found a new chief executive because it could not afford the expertise.
The pay is set by the public service employer - the State Services Commission - which says chief executive roles are 'job-sized' based on responsibilities, size of budget, and complexity of the work.
The language body reports to the Māori Development Minister, Te Ururoa Flavell; he is responsible for its budget, and he appoints the commissioners.
But when Te Manu Korihi asked his office for comment on not having a permanent leader and why it suffers from a high staff turnover, it said 'the Minister has no say of [sic] its operations as such'.
New Zealand First MP Pita Paraone is in a unique position to talk about the the lack of leadership at the Māori Language Commission.
He spent time in the top job before returning to Parliament to become an MP again after the last general election.
Mr Paraone said the position's salary band needed to be re-assessed.
"I think for the type of person and skills we're looking for, you're probably looking in the range of 250 [thousand dollars] per annum. Because what we need is someone with the language skills, but also the strong management skills that you would expect from any CEO of an organisation."
Pita Paraone said potential applicants were receiving good financial packages elsewhere.
"You probably have a number who are working in academic institutions like universities, and I know of a number who would be excellent CEOs for the Māori Language Commission".
"One of the reasons why they don't express an interest is because of the low salary compared to what they can get in the academic world."
Mr Paraone believes the Māori Development Minister doesn't want to give the commission any more money.
"They're probably wanting to exercise as much fiscal restraint as they can. But on the other hand if they're wanting to maintain or improve on the quality of service that the Māori Language Commission can make.. .they'll have to consider the very issue we're talking about."
Happy to help
The salary cap setter, the State Services Commission, said it could lend a hand in the search for a new CEO.
In a statement, the Deputy Commissioner Liz Sinclair said:
"The SSC has offered to provide the Board Chair of Te Taura Whiri i Te Reo Māori with further information or assistance that may be required to support the recruitment process for a new Chief Executive.
"All Crown entity Chief Executive roles are independently 'job-sized' based on factors including the level of statutory responsibility, budget responsibility and complexity of the role.
"The sizing of each chief executive role is carried out independently by organisations with specialist expertise."