In 2014, New Zealand exported $548 million of goods to Vietnam and imported about $493 million of goods from there, according to Statistics New Zealand data.
During the conference, plans to expand links in the education and agriculture sectors were also discussed, as well as an announcement that New Zealand would help train Vietnamese military for UN peacekeeping missions. Key said the co-operation was likely to involve joint training exercises after Dung requested New Zealand aid in training.
"Vietnam in 2014 officially joined in the forces of peacekeeping missions, the United Nations," Dung said.
"Vietnam is a new member and that is why we like experience and expertise in this area of co-operation, that is why in the spirit of a [comprehensive] partnership with New Zealand, I respectfully asked New Zealand to help Vietnam train the military officers of the Vietnamese in order to help them to engage in the peacekeeping missions of the United Nations."
The Trans-Pacific Partnership was also raised during the conference and Key said the deal was tracking well considering 12 countries were involved.
"I think on balance TPP negotiations are going well," he said. "These agreements always take a long time, so this is running at the sort of consistent timetable that we would expect of a quite complicated agreement."
Key said New Zealand wanted to see liberalisation in the agricultural area, which he singled out as particularly important.
"We see real benefits in free trade agreements when there is liberalisation of agriculture because typically that sees New Zealand working very closely with partners not to put their farmers out of business, but actually to encourage, improve and support the agricultural base in those countries."
Key said the next step for the trade agreement would be to see whether United States President Barack Obama could fast track the TPP agreement through Congress. If not, he said, the process could be more difficult.
Trade in 2014
• New Zealand exported $548 million of goods.
• Imported about $493 million of goods.
• Exports to Vietnam are mainly dairy products followed by wood.
• Food and beverage imports from Vietnam are growing - coffee, coconuts and crustaceans.
• Nearly 70% of Vietnam's GDP is from exports