ACC boss Scott Pickering had a pay rise from between $810,000 and $819,999 to between $830,000 and $839,999.
Telarc boss Philip Cryer had a rise from between $210,000 and $219,999 to between $250,000 and $259,999 - potentially a 24 per cent pay increase.
Hughes effectively warned the board members of the three entities that the Government could end their tenure, based on the report's information.
"While the board has the right to make these decisions, I do not believe increases of the magnitude given are warranted or justifiable in a public agency, especially where the increase follows previous increases over and above my advice," Hughes said.
"This information [in the report] can inform ministers' decisions about the tenure of board members."
Hipkins has asked the commission for advice on legal and regulatory changes - including possible changes to the Crown Entities Act - to contain growth in chief executives' pay, which he said had "gotten out of hand".
"We want to see a closing of the gap between high and low income earners and the public sector should be leading by example."
Prime Minister Jacinda Ardern said the Crown entities that did not have to follow Hughes' advice were effectively not "answerable to anyone".
"We're actively seeking what we can do to make sure they are answerable to at least, for instance, the State Services Commissioner. Something has to change."
Opposition leader Bill English also criticised the three entities' boards for acting against the wishes of the Government, but he questioned whether law changes were needed.
"The Government has power of appointment of the boards. If the Government is highly motivated, it will use that capacity to make sure pay rises aren't excessive."
The report showed that the average remuneration increase for public service bosses for the year to June 2017 was 2 per cent - up from 1.3 per cent the previous year
It was 2.7 per cent for Tertiary Education Institution and DHB chief executives, and 4.1 per cent for Crown entity chief executives, which were 2.8 per cent and 3.8 per cent the previous year respectively.
Over the same period, the average pay increase across the public sector was 2.2 per cent.
Hughes said the commission was developing a new remuneration policy to reflect a public service "underpinned by integrity, transparency, fairness, affordability and consistency".
"The new policy will recognise and reward motivations other than remuneration and will be more closely aligned to the delivery of high-quality services for New Zealanders."
It would take two to three years before the policy would impact pay packets, he said.
"There has always been, and should be, a differential between the pay of senior executives in the public and private sector."
Remuneration had to be fair to the taxpayers who pay the bill, he said.
"The aim is a remuneration policy that strikes the right balance between fairness to chief executives and the taxpayer and the need to attract and retain talent. And it must uphold public services principles."
Snapshot of chief executive remuneration for the year to June 2017:
• MBIE - Between $800,000 and $809,999
• University of Auckland - Between $710,000 and $719,999
• Police Commissioner - Between $690,000 and $699,999
• Treasury - Between $660,000 and $669,999
• Chief of Defence Force - Between $660,000 and $669,999
• Waitemata DHB - Between $620,000 and $629,999
The Senior Pay Report is based on total remuneration including base salary, performance-related payments, superannuation contributions and any other benefits received, such as additional leave.
Remuneration for government departments and ministry bosses is set by the State Services Commissioner, except for those set by the Remuneration Authority (SSC, Crown Law and GCSB).
Remuneration for Crown entity chief executives is set by their boards.
The Remuneration Authority sets remuneration for Officers of Parliament and chief executives of non-Public Service Departments (Police, NZDF) chief executives.
