Indonesia is unlikely to drop the death penalty, but is keen to make progress in other areas of human rights, Prime Minister John Key says.
Mr Key is in Indonesia to talk business, trade and terrorism and has had his first meeting with President Joko Widodo.
He says the discussion was wide-ranging, but included talk about the conflict in West Papua and Indonesia's use of the death penalty.
The country of around 255 million people has a chequered human rights record, including the use of firing squads.
On Monday, Amnesty International called on Mr Key to bring up the death penalty, which it says was used at least 14 times last year.
Indonesia's Attorney-General indicated last month that 16 people were set to face a firing squad this year, and they had a budget to execute another 30 in 2017.
Mr Key told Mr Widodo New Zealand was strongly against the use of the death penalty. But he doesn't expect changes any time soon.
"We registered our feelings that the death penalty is something we cannot and do not support, despite the severity of the crimes that people may have committed that they get the death penalty.
"It's not an issue I don't think the Indonesians are going to change their position on any time soon. They've got a major narcotics issue here in Indonesia, they've got a lot of Indonesians who are addicts and are trying to send a strong message, now we in New Zealand believe that can be said in a different way."
But Mr Key says Mr Widodo was more receptive to investigating any human rights breaches in West Papua, which he says was "proactively" raised by the Indonesians in the meeting.
Last month, Indonesian police were accused of arresting more than 1000 people at rallies in West Papua, demanding an independence referendum.
The conflict over West Papua - part of Indonesia's easternmost Papua province on New Guinea island - has been going on for decades. The population is ethnically distinct from the rest of Indonesia.
Prior to the meeting, the Green Party urged Mr Key to discuss the "deteriorating human rights situation" in West Papua.
Mr Key said Mr Widodo and was "keen" for him to understand the situation and the issue of human rights.
"They raised the point specifically about human rights, and said if there are specific issues with human rights, then they take up those issues, they investigate them and make sure they're not repeated.
"They seem to be quite keen to have greater transparency.
"We don't dispute the issue of territorial rights of Papua. I think that's been a long-standing New Zealand Government position - that we recognise territorial rights - but on the broader issue of human rights, we said to them that's a matter that's always of great concern to New Zealanders."
Mr Key said Mr Widodo and the country's Foreign Minister Retno Marsudi "gave us assurances they were observing human rights there".
Asked whether he believed them, Mr Key said they'd made "genuine" progress, and weren't dismissive of New Zealand's concerns.