New Zealand Prime Minister Chris Hipkins reluctantly voiced his support for co-hosts Australia at the Women's World Cup on Tuesday following his own country's elimination.

New Zealand's Football Ferns bowed out after Sunday's goalless draw with Switzerland, while Australia reached the knock-out stages following a 4-0 thumping of Canada on Monday.

The tournament is being hosted by both New Zealand and Australia, whose women's football team is nicknamed the Matildas.

Hipkins laughed, then looked awkward, when asked by an Australian journalist if it was now time for New Zealanders to support their trans-Tasman neighbours at the Women's World Cup.

"I'm obviously very supportive of the trans-Tasman relationship, but I just think Kiwis should continue to pay an interest in the tournament," he replied.

"It's a great thing for New Zealand and Australia to be co-hosting.

"It's good to see that, even though our Kiwi team haven't made it any further in the tournament, that there's still a great degree of enthusiasm and support for the games that are still going."

But Hipkins was more direct when the same Australian reporter asked why it was so hard for New Zealand sports fans to support Australia.

After being prompted to come out and say it, Hipkins reluctantly said: "Go the Matildas".

"Look, I don't know. There's something in it – isn't there? – about Kiwis just backing an Australian team, but of course we wish our Aussie mates the best," he added.

Looking slightly sheepish, Hipkins joked that he expected to hear from Australian Prime Minister Anthony Albanese over his backing of the Matildas.

"I'm going to get text messages from 'Albo' about that probably, right?" Hipkins added.

However, he was adamant when asked if he would rather England win the World Cup than Australia, saying: "I wouldn't go that far."