Prime Minister Jacinda Ardern has kicked off a string of royal appointments with a meeting at Clarence House with Prince Charles and Camilla.

And as reports circle that Prince Harry and his wife-to-be Megan Markle could visit New Zealand in October while in Australia for the Invictus Games, Ardern said no formal invitation had been issued "but there is a standing invitation for members of the royal family".

Ardern, who was accompanied by partner Clarke Gayford, said her talk with Charles and Camilla had been "a fantastic conversation".

Britain's Prince Charles poses with Ardern. Photo / AP
Britain's Prince Charles poses with Ardern. Photo / AP

"It really demonstrated to me the degree of knowledge and interest that the royal family genuinely has in New Zealand and topical issues."

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She said that interest was clear from the visits by royals to New Zealand.

"They have a real keen eye on issues that are affecting us, natural disasters that are affecting us and that conversation reinforced that for us today."

Ardern is set to meet Charles' mother Queen Elizabeth tonight at Buckingham Palace.

She was undecided whether to mention the death of the Queen's last corgi, Willow. Ardern's cat Paddles died last year after being hit by a car.

Canada's Prime Minister Justin Trudeau, left, takes a selfie with Mayor of London Sadiq Khan, center, and New Zealand's Prime Minister Jacinda Ardern at City Hall in London. Photo / AP
Canada's Prime Minister Justin Trudeau, left, takes a selfie with Mayor of London Sadiq Khan, center, and New Zealand's Prime Minister Jacinda Ardern at City Hall in London. Photo / AP

"I've genuinely wondered about that. When I lost a pet I had it raised with me and I always found it to be kind that people thought through and considered those kind of issues. I'm going to give it a bit more thought.

British Prime Minister Theresa May, left, speaks with New Zealand Prime Minister Jacinda Ardern in the gardens at Downing Street. Photo / AP
British Prime Minister Theresa May, left, speaks with New Zealand Prime Minister Jacinda Ardern in the gardens at Downing Street. Photo / AP

"It is very recent and I certainly wouldn't want to cause any additional sadness by raising it."

The four met at Clarence House. Photo / AP
The four met at Clarence House. Photo / AP

She will take some good news to the Queen - that she will support the Queen's successor Charles taking over as Head of the Commonwealth after her reign ends.