Europe is stronger with Britain in it and if New Zealand wasn't so far away it would want to join such a union, Prime Minister John Key says.

Mr Key has met with British Prime Minister David Cameron, with the looming Brexit referendum a topic in a "wide-ranging" discussion.

Both leaders are in Washington DC before the two-day Nuclear Security Summit.

"New Zealand's perspective is that it is up to the British people to decide. But we certainly think it is a stronger position for Britain to be in Europe. We see Europe as an extremely important continent that needs strong leadership. We think Britain provides that leadership," Mr Key said during a joint press conference after today's meeting.

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"We are currently going through the process of wanting to sign a free trade agreement with Europe, because it is the home of 500 million people, and a huge amount of middle-income consumers. Both David Cameron and [German Chancellor] Angela Merkel have been the leaders of looking to get New Zealand into a free trade agreement, so we think we are well served by that.

"As somebody who has lived in the United Kingdom for a long period of my working life, I guess all I would say is if we had the equivalent of Europe on our doorstep, New Zealand as a country would be looking to join that, we certainly wouldn't be looking to leave it. But the British people will make up their own mind."

A referendum on whether Britain should remain in the European Union will be held on June 23. Mr Cameron wants Britain to stay in the EU.

At today's press conference, he said he and Mr Key had discussed the work being done in Afghanistan to train army officers, as well as similar work being done in Iraq to counter the Islamic State.

If we had the equivalent of Europe on our doorstep, New Zealand as a country would be looking to join that, we certainly wouldn't be looking to leave it.

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The economic links between Britain and New Zealand were also covered, Mr Cameron said, as well as issues of migration and movement, "which is very important between our countries".

"It is a very strong relationship, it's getting stronger all the time," Mr Cameron said.

Mr Key has previously expressed unhappiness at a change that will see certain New Zealanders in Britain charged a health surcharge from next week.

Stricter visa rules that also start from April 6 will see non-European Union migrants working in the UK kicked out after five years if they earn less than $76,000 a year.

About 200,000 Kiwis are living in the UK. Numbers of those staying long-term have fallen from about 18,000 in 2000 to 8500 in 2014, mostly as a result of previous changes that have restricted job opportunities.

Earlier, Mr Key met with Indian Prime Minister Narendra Modi. Bolstering economic ties with India, which has a population of about 1.26 billion, was a main topic of conversation.

Mr Key told Newstalk ZB's Mike Hosking a number of areas could be worked on.

"It is potentially more students coming to study in New Zealand, he actually made the point of saying he personally wants to see more Indian students studying in New Zealand, and he thought we should actually up our marketing and make the case even stronger.

"Tourism: he sees tremendous opportunities in that space. They are the largest producer of milk in the world, but they don't have the capability like we do in terms of the further production of that milk."

On the chances of the Trans-Pacific Partnership progressing, Mr Key said last night he was at a dinner attended by the US chief negotiator Michael Froman. He said Mr Froman believed it could be legislation before the new US president is sworn in next January.

Hillary Clinton and Donald Trump say they oppose the TPP. Mr Key has said the US could not afford to not be part of the trade deal.

The Nuclear Security Summit is a President Obama initiative to co-ordinate international efforts to prevent terror organisations from acquiring nuclear weapons or material.
Leaders from more than 50 countries will attend the summit.

Mr Key has attended all three summits since the first in 2010, and said they were worthwhile.

"The real issue is, there haven't been the same global treaties and conventions of the way of dealing with this nuclear material, that there has been in a lot of other things that affect the world, because it has been the responsibility of individual countries.

"The real risk is that this material gets into the wrong hands. You get an Isil or group like that, they get control of some nuclear material and that could have catastrophic implications."

Steps had been taken through the previous summits to support a more unified approach, Mr Key said, and he was hopeful of more progress at this year's meeting.