Ms Ardern confirmed the meetings but disclosed minimal details after arriving in the UK, saying she will “share the sorrow that New Zealand has” with the new monarch.
“I’ll simply share the sorrow that New Zealand has and pass on our deepest condolences,” the visiting PM said at a press conference in London.
“At the end of the day, although this is a period of transition for him, he has also lost his beloved mother. For us and New Zealand, that’s first and foremost.”
Ms Ardern, who said she is planning to attend the Queen’s lying in state at Westminster Hall ahead of the funeral, also confirmed she will meet with Liz Truss.
The visiting PM said the Queen’s death and new King will be the “focus of conversation” when she and Ms Truss meet.
She said she will also likely discuss Ukraine and the UK’s free trade agreement with New Zealand.
“I am sure we will also transact our relationship as well, but it is all within the context of the week of mourning that the UK is currently in,” she said.
Meeting William will be an opportunity to repay his support of New Zealand in 2019, when the royal flew to the country following the Christchurch massacre, Ms Ardern said.
“The Prince of Wales has always been there for New Zealand in its times of grief,” she said.
“He’s been there for us in our times of grief and so this is a time for us to be there for him and his family too.”
There won’t be formal bilaterals in the way we normally recognise them
Several hundred dignitaries from around the world will be in London to pay their respects to the Queen, in what is set to be one of the biggest logistical and diplomatic events in the UK in decades.
No 10 declined to describe the conversations with allies as formal bilateral meetings, and instead portrayed them as chats to offer condolences over the Queen’s death, during which politics is likely to come up.
The Prime Minister’s official spokesman said: “There won’t be formal bilaterals in the way we normally recognise them.
“But we will have a significant number of world leaders, heads of state in the country. She will be meeting a small proportion of those over the weekend.
“These will be opportunities to discuss memories of Her Majesty, but in some instances it will be the first time they’ve met since she became Prime Minister.”
A UK meeting with US President Joe Biden, who will attend the funeral with First Lady Jill Biden, would ease the pressure on Ms Truss’s expected visit to New York for a UN summit next week.
Chevening will be used as one base for meetings rather than the Prime Minister’s country residence of Chequers, which is said to be undergoing routine maintenance work after Boris Johnson’s exit.
French President Emmanuel Macron confirmed his attendance at the funeral after offering his country’s condolences in a call to the King.
Mr Macron tweeted about the “unbreakable” ties between France and the UK as he promised to “strengthen” the relationship between the UK and France by “following the path” of the late Queen.
It is unclear whether he will be among the world leaders Ms Truss will meet, but if they do it will be a chance for her to clear up where their relationship stands.
During her campaign to become Tory leader, she sparked controversy by saying the “jury’s out” over whether Mr Macron is a “friend or foe”.
There have also been suggestions she could speak to Irish Taoiseach Micheal Martin on the margins of the funeral, amid strained relations between the two countries over the continuing row about the Northern Ireland Protocol.
About 500 dignitaries from around the world will head to London for the state funeral.
They will join members of the royal family, UK prime ministers past and present and key figures from public life at Westminster Abbey – which can hold about 2,000 people – at 11am on Monday.
Representatives from the Commonwealth realms – the nations which had the Queen as head of state – will also be able to attend the committal service in Windsor Castle.
Male dignitaries at the funeral will be advised to wear morning dress or dark lounge suits with a black tie, with dark day dresses and hats for female mourners.
National dress may also be worn, while serving military officers can wear ceremonial uniforms without swords.
The leaders of most Commonwealth countries are expected to attend the funeral.
Ms Ardern’s Canadian and Australian counterparts, Justin Trudeau and Anthony Albanese, have also confirmed their attendance.
But India’s prime minister Narendra Modi, who landed in Uzbekistan on Friday morning for a meeting with Russia’s President Vladimir Putin there this week, is not expected to come to the UK, with President Droupadi Murmu being dispatched instead.
Germany’s President Frank-Walter Steinmeier, Italy’s President Sergio Mattarella and Brazil’s President Jair Bolsonaro are among those attending, along with the president of the European Commission, Ursula von der Leyen.
King Felipe of Spain and his wife Queen Letizia are among the European royals who will attend.
Emperor Naruhito of Japan is also set to travel to London for what will be his first overseas trip since ascending the throne in 2019.
Local media said Turkish foreign minister Mevlut Cavusoglu will attend in place of President Recep Tayyip Erdogan.
Invitations to the Queen’s funeral have not been sent to Russia or Belarus against the backdrop of the invasion of Ukraine.
Taliban-ruled Afghanistan has also been excluded, as has Syria and Myanmar.
The seating plan, which could prove to be highly complicated due to the various protocol and political issues thrown up by a gathering of this size, is yet to be finalised.