The UK and New Zealand will launch a "people-to-people dialogue" to discuss issues including improving opportunities for citizens to live and work in each others' countries.
Watch the media conference:
UK Foreign Secretary Boris Johnson has met Prime Minister Bill English and Foreign Minister Gerry Brownlee in in Wellington, as Britain seeks to progress its exit from the EU.
Mr Johnson told a media conference that the UK would consider measures on secondments and exchanges with a view to "firming up what is already a very, very profound friendship".
Mr Brownlee said the governments also agreed to deepen collaboration on the issue of social investment, taking a data-driven approach to supporting effective social policy.
Talks this morning covered North Korea, the fight against terrorism and sharing of intelligence, Mr Johnson said. "To [an] almost embarrassing degree there was a total failure to disagree on any point of substance," he told the gathered reporters.
He described the dynamism and resilience of Kaikōura residents in rebuilding after last year's earthquake as admirable.
He hoped the war memorial unveiled yesterday in Wellington would remain a symbol of continuing friendship between the countries.
Mr Johnson earlier said it was amazing to come to the other side of the world and meet a government and people his country had so much in common with.
He said the UK wanted to do a big free trade deal with New Zealand, which would be "at or near the very front of the queue" for such deals after Brexit.
Mr English said New Zealand had its own interests in what happened with the UK, and respected the process that was under way as it withdrew from the EU.
Mr Johnson suggested to Morning Report that Britain could look at introducing some sort of special visa for Commonwealth countries once that process was complete.
His comment followed what the foreign secretary called "bureaucratic foul-ups", where people who had paid extra money for urgent visas found they were waiting 30 to 40 days rather than the intended 10.