New Zealand have been sent crashing out of the Women's World Cup on goal difference after being held to a 0-0 draw against Switzerland on Sunday.

Norway's 6-0 thrashing of the Philippines in the other Group A game in Auckland put them level on four points with New Zealand but second on goal difference. Switzerland advanced to the knockout stages as group winners on five points.

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The results meant New Zealand, who stunned Norway in their opening match before losing to the Philippines in their second, became the first Women's World Cup hosts to exit in the group stage.

Roared on by a near-capacity crowd of 25,947 at the indoor Dunedin Stadium, New Zealand lacked nothing in effort but could not find the goal they needed to progress.

"I can't ask any more of the players. There's a lot of tears out there but they should be so proud," New Zealand co-captain Ali Riley said. "We fought really hard... There's such disappointment but I want everyone to be proud of what we've achieved.

"I really think that we've inspired the country. I hope that little girls across New Zealand and the world now will start playing sport and feel like they can achieve whatever they put their mind to and just dream bigger.

"I just hope that this opens so many doors and opportunities for young girls. We wanted to inspire, we wanted to honour the Ferns that came before us and this team did that. I'm so proud of them."

Switzerland started the match on the front foot and midfielder Ramona Bachmann skipped past several defenders before her shot was blocked, but they were unable to keep the momentum going while New Zealand gradually upped the tempo.

Jacqui Hand and Olivia Chance both hit the post while Katie Bowen's shot was blocked as New Zealand pushed for an opener and looked more likely to score.

Switzerland looked more comfortable after the break, with Seraina Piubel slicing a left-footed shot wide off the mark before being ruled offside, while New Zealand struggled in the final third.

Malia Steinmetz's strike from the edge of the penalty area was saved as New Zealand became increasingly frantic in their efforts -- goalkeeper Victoria Esson headed wide in the closing minutes -- but Switzerland held firm and saw out the draw.

"I know [it's] super emotional now because everybody's disappointed about the result but this team can be so proud," New Zealand coach Jitka Klimkova said. "There are so many positives that we are taking away from the whole experience.

"Our crowd showed how much they care... I feel that the nation is behind us and I really am thankful for that because they are part of this journey and part of us."

Switzerland and Norway will face either Spain or Japan, who play their Group C decider on Monday, for a place in the quarterfinals.