They met at the Edgewater Resort and Spa on Saturday for about an hour.
Browne said they were grateful for the opportunity to discuss key national issues with the visiting delegates after being taken off the programme because of limited time.
The delegation had to cut their visit short because of commitments with the Parliament in New Zealand this week.
Opposition MPs Tamaiva Tuavera, Selina Napa and Agnes Armstrong were also part of the meeting, while the visiting delegation had Peters, New Zealand Police minister Stuart Nash and Parliamentary under-secretary for foreign affairs Fletcher Tabuteau.
“We had a productive meeting. We talked in general and particularly they are concerned with their role and the fact New Zealand does not want to interfere with the internal governance of the Cook Islands which we accept,” Browne said.
“They agreed to look at ways to improve our Parliament, meaning that they would continue to provide assistance in workshop for Parliament members, Speaker, deputy Speaker and Clerk of Parliament.”
Browne said the Opposition also raised the issue of the number of sitting days in Parliament.
She said they were told that New Zealand Parliament normally sat for 40 weeks which was a major contrast to the sitting days in the local Parliament.
“We also talked about the law and order, some matters with the police, the drug issue and how best they can assist us in detecting and arresting those who are spreading drugs in the Cook Islands,” Browne said.
“They said they are looking at ways to provide more drug dogs and also try and improve the capacity of our police to detect drugs coming through the border.”
Browne said they also raised the issue of New Zealand arrest warrant on a local MP and were told the onus was on the Cook Islands Justice ministry and Police to coordinate with their New Zealand counterparts on this matter.
“I think the point of our discussion was to ensure good governance for the Cook Islands and I think their impression which I also see as our role, to be a good Opposition so that we have a better government.”
New Zealand Police minister Nash also said the discussion with the Cook Islands Opposition party members went well.
“One thing I find with politicians no matter if they are Opposition politicians in New Zealand or from the Cook Islands, everyone wants what’s best for the country,” Nash said.
“They have different ideas but when it comes to things like methamphetamine then we all tend to come together, and say ‘we need to work together’ because if we bring politics into this then often what happens is you don’t get an ideal outcome.”