The Cook Islands prime minister, Dr Robert Woonton, says he is powerless to prevent a New Zealand man, Mark Lyon, from staying in Rarotonga.
Lyon has a criminal record in New Zealand but Dr Woonton granted him a 12-month residency permit after Lyon paid a 150-thousand New Zealand dollar bond through his lawyer Norman George.
Dozens of people marched through the Cook's capital at the weekend to protest at the decisions.
But Dr Robert Woonton, who is in New Zealand and speaking on TVNZ's Breakfast programme, says Lyon has the law on his side.
"We have no legal fetters to stop him, neither can we deport him for that matter. Our law categorically says if he applied to me while outside of the country I have the power to stop him from entering the country."