WELLINGTON (REUTERS) - When recently returned New Zealander Lara Barclay talked to fellow Kiwi expatriates in Australia, it was her country's success in tackling coronavirus that came up again and again and the crisis role of prime minister Jacinda Ardern.

Support from New Zealand's million-strong diaspora - equal to a fifth of the country's resident population - could prove a surprise boost for Ms Ardern as the Labour Party leader seeks re-election at an Oct 17 poll.

"They thought New Zealand's response was fantastic," said Ms Barclay, a victim support worker. "Every New Zealander I knew in Australia bar one ... were super impressed by New Zealand's response and by Jacinda."

Labour is widely expected to retain power next month and hopes to rule without the support of a coalition partner, although the opposition National Party has been clawing back support in recent polls.

Overseas polling began on Wednesday (Sept 30), but a big unknown is how many expatriates will actually vote.

Just 10 per cent of eligible overseas voters cast their vote in the last election in 2017, but analysts say Ms Ardern's global profile from her promotion of issues such as social justice and equality, may draw more support.

"Ardern's got on to the front pages of world media and has been covered in way that no other New Zealand prime minister has been before," said Mr Geoffrey Miller, analyst at the political website Democracy Project.

"It wouldn't be a surprise if more New Zealanders living overseas decide to vote for Ardern, or may be just decide to vote in general," he said.

Tough restrictions to contain coronavirus limited New Zealand's total cases to less than 1,500 and just 25 deaths, far fewer than other developed nations, and the virus is largely contained.

The quick crisis response follows plaudits for 40-year-old Ms Ardern's compassionate and inclusive response to an attack by a white supremacist at two mosques as well as a fatal volcanic eruption.

She is even tipped as a front runner to win the Nobel Peace prize, according to a UK betting agency.

DOMESTIC DIFFICULTIES

Ms Ardern won't have it all her own way. Analysts say Labour has largely failed on its big ticket policy promises like providing affordable housing, reforming tax and building key infrastructure.

She faces National Party leader Judith Collins, known as"Crusher Collins' for her tough-talking personality, who took over as leader in July.

Ms Collins, 61, is a seasoned politician well known to the electorate, who is mostly associated with issues such as law and order, and infrastructure.

She has made efforts to connect more strongly with the farming community, but her appeal remains local while Ms Ardern is known for how she portrays New Zealand to the world, said Mr Richard Shaw, of Massey University.

"Ardern has turned that feeling right up to maximum volume, while Collins does not get any play in that space," Mr Shaw said.

About 67,000 New Zealand voters have so far enrolled overseas, election officials said. This compares with about 61,000 who voted in the 2017 election, out of about 2.6 million votes in total.

Voters still have until mid-October to register and referendums on legalising cannabis and euthanasia could encourage more to take part.

The majority of those enrolled are in Australia, at nearly 60 per cent, followed by the UK at 17 per cent and more than 6 per cent in the United States.

With the latest polls showing support for Labour at 47 per cent, Ms Ardern has urged New Zealanders in Australia to vote.

"Every single vote counts, including those Kiwis in Australia," she told broadcaster Channel Nine. "They're almost the equivalent to a seat."