Prime Minister John Key says he will signal New Zealand's deep opposition to the death penalty in Indonesia when he meets with its President later this evening.
Trade, regional security and the threat of terrorist attacks will also be high on the agenda as Mr Key begins a two-day trip to Indonesia today, visiting Jakarta and Surabaya.
Mr Key said President Joko Widodo had launched a strong campaign against drugs in Indonesia, and the threat of the death penalty was part of that.
"While we absolutely have sympathy for what they are dealing with and while those who have committed crimes should be held to account, there's a better way of doing that than by using the death penalty.
"There will also be a discussion about Papua, I mean those issues are ones where I think the President has been trying to have more openness in the situation."
He said every global leader was concerned at the moment about the rise of Islamic State.
"And their capacity to want to recruit these individual soldiers anywhere around the world and also the issue of returning foreign fighters, so I think both Indonesia and France potentially have quite large numbers of foreign fighters and that presents an added complication for them."
After their meeting this evening, Mr Key and President Widodo will sign an agreement on renewable energy and another to combat illegal fishing.
Mr Key said during the meeting he also planned to discuss trade barriers Indonesia imposes on some New Zealand exporters.
"It's a big potential market for us, 250 million people, young population so we see a lot of opportunity there and that is part is what we are going to talk to them about, they are part of the ASEAN-Australia-New Zealand Free Trade Agreement and so we want to continue to push that."
New Zealand and Indonesia are part of a 12-country free trade agreement which came into effect in 2012.
While that deal has reduced tariffs, it is now the non-tariff barriers that are a serious problem for some New Zealand exporters.
Indonesia used to be New Zealand's second biggest market for beef, but those exports have declined by 84 percent since 2010.
Alliance Group chairman Murray Taggart said the restrictions had been hugely frustrating for farmers.
"Beef exports are at a very low level to Indonesia at the moment, primarily because of the difficulties of getting consistent access to the market.
"You're trying to do programmed business over the course of the year and it's very difficult to do that for a market that is there one minute and gone the next."
The government estimated the accumulated trade impact to the beef sector alone was now up to $1 billion.
In 2014, New Zealand and the United States together took Indonesia to the World Trade Organisation over the restrictions and a decision was expected later this year.
Lance Sheppard from Export New Zealand said corruption in Indonesia had also been a problem in the past, but that was changing.
"Government departments are still very bound by historical ways of doing business, but certainly in the private sector a lot of these private companies are now being run by the next generation of business leaders within Indonesia who are young, who have been educated overseas, who are very very aware of how they must conduct themselves if are going to thrive in the global economy."
Amnesty International campaigns director Meg de Ronde said John Key must not only raise the issue of Indonesia's poor human rights record while he was there, but also advocate for the country to prioritise humans rights protections.
"This was something that President Widodo campaigned on when he came to office in 2014, and in particular we are very concerned to see the resurgence of the death penalty in Indonesia.
"We are asking Prime Minister, John Key, to advocate that Indonesia immediately puts a moratorium on executions and moves to abolish the death penalty."
Mr Key is due to meet with President Joko Widodo Monday evening New Zealand time.