Deputy Prime Minister Winston Peters has welcomed Robert Mugabe's resignation - saying it is a critical point in Zimbabwe's history.

Mugabe stepped down from the presidency today after 37 years.

"This moment will be seen as a critical point in the history of Zimbabwe. The Zimbabwean people have voiced their support for change in a peaceful way," said Peters, also Foreign Minister.

"New Zealand has made its position on the Mugabe regime clear over the years. Zimbabwe has suffered enormously under Robert Mugabe's presidency through economic oppression, corruption and a blatant disregard for democracy and human rights."

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Peters said New Zealand had travel bans on Mugabe and his wife Grace because of the "destructive nature" of the politician's Government.

"The Zimbabwean people have an opportunity to hold free and fair elections as soon as possible to determine the future direction of their country.

"New Zealand supports the efforts of the Zimbabwean people to uphold democracy and to return to a prosperous and vibrant country free of oppression."

Prime Minister Jacinda Ardern said the resignation was a relief after "37 years of oppressive rule".

"It's obvious from what's happening in Zimbabwe that that has been widely greeted with a huge amount of anticipation and happiness.

"It's pleasing to see change afoot. Now the focus has to be on democratic elections."