"It is potentially a very large market," Key told the delegation last night. "[More than] 150 million of them are young, probably under 25-30, and they are going to get wealthier and demand more of what we produce."
Two-way trade between the countries is currently worth $1.6b, and the two countries have set a goal of $4b by 2024.
However, there have been some obstacles.
New Zealand, along with the United States, has laid a complaint with the World Trade Organisation (WTO) against Indonesia's import restrictions. The case is ongoing.
Indonesia's tariffs and other restrictions led to a 80 per cent fall in New Zealand's beef exports since 2010.
Key alluded to the dispute in his speech to the delegation, saying New Zealand's meat industry had been "going through a few challenges". Speaking to reporters afterwards, he said the matter was likely to come up in bilateral talks with President Widodo today.
"We will certainly be raising the broader issue of wanting to have what we believe is fair access for beef.
"This was a very big market from our perspective four or five years ago. We have been effectively cut out of that market in recent years."
Trade Minister Todd McClay, who is also in Jakarta, downplayed the impact of the WTO case on the two countries' relationship.
"We have a very mature relationship with the Indonesian Government," he said.
"New Zealand and a number of countries have taken a case but at the same time we continue to co-operate with Indonesia on many other fronts.
"I don't expect that this will be an issue insofar as the relationship's concerned."
Key and Widodo are also expected to discuss developments in the South China Sea, counter-terrorism, and people-smuggling.