German Chancellor Angela Merkel says she will back a New Zealand push for a free trade agreement with the European Union - words that will be music to Prime Minister John Key's ears.

Speaking to media during her visit to Auckland today, Dr Merkel said Germany would champion New Zealand's cause.

Merkel in New Zealand: App users click here for gallery

"I think we should also come out in favour of a free trade agreement between the EU and New Zealand. New Zealand has such agreements with China and other areas of the world.

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"As a member of the European Union, Germany is very much championing, despite the great distance that separates us, to foster our trade relationships, to bring forward trade with the European Union."

She said she was impressed by New Zealand's growth, saying it was because the country was open minded and encouraged free trade.

Mr Key said Germany was already a critical trade partner and two-trade was now larger than with the United Kingdom. However, there was scope to do more and he had spoken about NZ's aspirations for a free trade agreement with the EU. New Zealand is one of only a handful of countries in the OECD which does not have trade talks underway although a low level political agreement is in place.

Mr Key said the pair discussed a range of issues including their respective relations with China, Islamic State, Syria, and Ukraine. Dr Merkel said they spoke of the challenges of fighting terrorism. New Zealand and Germany have a similar stand on Islamic State - Dr Merkel said Germany had provided some training to Kurdish troops and was considering what to do next. However, like New Zealand, she did not expect Germany to play a combat role.

Work of greater links in science and technology was proposed with Germany and the PM launched a new fellowship programme with Germany to allow New Zealand to bring German leaders to NZ each year.

Prime Minister John Key has assured German's Chancellor Angela Merkel her cellphone was not being tapped while she was in New Zealand.

Dr Merkel criticised the United States for spying on its friends after learning the NSA had tapped her personal cellphone in the past.

New Zealand is part of Five Eyes under which it shares intelligence with the United States. Dr Merkel was asked about that relationship and said she was aware NZ was part of the Five Eyes and had a close intelligence relationship with the United States.

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A slightly embarrassed Mr Key said New Zealand also shared some intelligence with Germany although it was not part of Five Eyes.

"I think there are some lessons have been learnt in the past. If I was the Chancellor I would rest assured she has nothing to fear on her phone calls in New Zealand. She's a great friend of New Zealand and if we have any questions of her I'll just ask her. I think that would be the fastest way of resolving any issue. So there's nothing to fear."

Dr Merkel said she was not opposed to intelligence sharing and Germany and the USA also shared information that had been critical in stopping terrorist and cyber attacks.

"So we depend on this kind of close cooperation. But it is true as a close partner and friend of the United States we believe the ratio between the kind of surveillance they have been carrying out and privacy of the individual is perhaps a bit out of kilter."

She said working on intelligence did not preclude them having differences of opinion sometimes and when that happened she raised them openly with US President Barack Obama.

Merkel also thanked New Zealand for its support of the sanctions put in place against Russia after its incursion into Ukraine.

New Zealand has halted its free trade agreements with Russia after that happened earlier this year.

Both Key and Merkel are due to head to Australia for the G20 tomorrow which Russian President Vladimir Putin will also attend. Putin and Australia's Prime Minister Tony Abbott have already crossed swords over whether Russia was implicated in the downing of the Malaysia Airlines flight, which was carrying more than 100 Australians.

There has been controversy in recent days because Russia was sending warships towards Australian territory in an apparent show of muscle.

Dr Merkel noted that, saying Russia was clearly trying to show it had a presence.

"But what I find far more worrying is the violation of the territorial integrity of Ukraine."

Mr Key said the ships were in international waters so were free to move as they wished. "Whether that's necessarily helpful is another matter."

Mr Key said New Zealand was a long way from Russia but did have concerns about the instability it was having on growth in Europe.

"We, like the rest of the world, look to Europe to be a strong growing partner to underpin global growth. So concerns in the Ukraine and wider region are obviously of concern to New Zealand."

Dr Merkel expected it to be raised on the sidelines of the G20 meeting.