The Cook Islands opposition Democratic Party is calling for a special meeting of the Crimes Bill Select Committee.
This is to allow renewed debate of a controversial bill that would criminalise same-sex relations.
In a statement, the Democratic Party said clauses breaching international human rights declarations had gone unchallenged.
A special meeting is needed so the committee can be given legal advice on the Crimes Bill before it makes a recommendation to parliament, it said.
The statement comes after New Zealand LGBTQI advocates threatened to boycott the Cook Islands as a tourism destination over the bill.
The proposed amendment to the Crimes Act 1969 maintains a clause under which Cook Islands men can be jailed for five years for engaging in what's dubbed "indecent acts" with other men. People hosting these acts in their premises face up to ten years jail.
"The full implication of reinstating and expansion of anti-gay law also has to be fully examined," the Democratic Party said in its statement.
"The Democratic Opposition also has concerns regarding breaching the United Nations Declaration of Human Rights to which the Cook Islands is a signatory and the nation's own Constitution."
The select committee had initially struck out the controversial laws, but backed down after seeking advice from the public. LGBTQI advocates said a submission from the country's influential churches, which recommended maintaining criminalisation, was instrumental in the select committee's decision.
Tingika Elikana, the committee's chair, told RNZ Pacific earlier this month the final report to parliament would be submitted in February.