Brash and Rich, along with Dunedin author Lynley Hood, have written to the minister asking him to consider a fresh inquiry.
Hood wrote a book about the Christchurch Civic Creche case.
Ellis was convicted in 1993 on 16 counts involving sexual offences against children in his care at the creche, and sentenced to 10 years in prison. He was released on parole in February 2000 after serving two-thirds of his sentence.
The verdict was upheld twice by the Court of Appeal, and again by a ministerial inquiry conducted by former Chief Justice Sir Thomas Eichelbaum.
In a letter to Power, the trio say the Christchurch Civic Creche case remains a stain on the New Zealand justice system.
"In our view, the time is long overdue for the minister responsible for our justice system to demonstrate the political will and moral courage necessary to ensure that a comprehensive and genuinely independent inquiry is held into what is widely regarded as New Zealand's most egregious miscarriage of justice," they say.
"That the wrongs done in the creche case have not been righted after all this time is nothing short of a scandal.
"A full inquiry is needed to ensure that the mistakes made in the creche case will not be repeated."
They ask Power to consider appointing an Australian judge to reconsider the case, believing it would be difficult for a New Zealand judge to approach it without prior knowledge or involvement.
The trio also ask that a judge be given the power to recommend a pardon for Ellis if he or she found that a miscarriage of justice had occurred.
Rich said an inquiry into the Ellis case was essential. "Two former prime ministers, 12 law professors, 10 Queen's Counsel and thousands of other petitioners have already expressed their concerns. This case will not go away until a final review is done."
Power did not return calls from The Press yesterday.