The Cook Islands opposition leader says the prime minister should have taken action over MP Albert Nicholas, who is wanted by police in New Zealand.
Mr Nicholas failed to appear in the Manukau District Court last month to face a charge of unlawfully taking a motor vehicle.
Tina Browne said she had been told by Cook Islands police that they were also investigating Mr Nicholas on an unrelated matter.
The MP bolstered the governing Cook Islands Party's thin majority when he was sworn in earlier this month.
Ms Browne said Prime Minister Henry Puna should have handled the matter differently.
"Well I think he should have done a little bit more than just think that Albert is a number for him. I think he should have taken some steps to get him back to New Zealand to comply with his appearance in court, perhaps wait until the investigation on him has been completed, and see then what happens," she said.