Muller's deputy Nikki Kaye and former finance spokesperson Amy Adams say they will not seek reelection at the September 19 poll.

Both say their retirements aren't related to the selection of conservative Judith Collins as Muller's successor.

Kaye - a supporter of gay marriage and advocate for climate change policies - represents the liberal wing of the centre-right party but says she will campaign for Collins.

"I believe Judith is absolutely the right leader for the party at this time and I will be supporting Judith and the party to win this election," Kaye said on Thursday.

Adams had responsibility for the party's COVID-19 recovery portfolio under Muller but its removal with his departure led her to reaffirm her departure.

"With Todd Muller's decision to resign the leadership, the most important issue for our party was to get a strong and effective leadership team in place without delay and I am proud at the way in which the caucus managed this," she said.

The party's week of turmoil began on Tuesday with Muller's shock resignation. The 67-year-old former businessman blindsided colleagues when he announced his resignation in an early-morning statement, citing health issues.

Muller had taken over the leadership 53 days earlier in a move prompted by the party's stagnant polling, but his tenure was short and troubled.

Soon after his elevation, he was photographed in his office among memorabilia which included a Make America Great Again cap and was accused of a dog-whistle to his party's right-wing supporters. He then named a shadow cabinet criticised for its lack of diversity; the highest-ranked person of colour was 17th.

Muller's greatest challenge came when an MP leaked private health details of New Zealand COVID-19 patients to news media. It wasn't published and the MP resigned, but Muller struggled to distance himself from the scandal.

National has also struggled against the popularity of Prime Minister Jacinda Ardern and the broad approval of her government's handling of the pandemic.

New Zealand has gone weeks without a community-spread infection, nearly all lockdown restrictions have been lifted and public life has largely returned to normal.

National's pitch to voters has been that it has a more competent team than Ardern's. But the departures of several high-profile MPs have begun denting that assertion.

Australian Associated Press