Health and hygiene giant Essity and Australian packaging and recycling business Visy have been unable to agree terms for new deals with Kiwi workers.

In Kawerau, around 145 mill workers have been locked out and stood down indefinitely by owners Essity.

The mill supplies a majority of New Zealand's toilet paper, and Pulp and Paper Union Kawerau secretary Tane Phillips said the impasse could see Kiwis run short.

"We're the only place that actually makes it from scratch in New Zealand," he told AAP.

The mill is the major employer in Kawerau - an inland Bay of Plenty town - and produces roughly 70 per cent of New Zealand's toilet paper.

Supermarkets are monitoring the situation, with Woolworths-owned Countdown working with Essity to manage supply.

A spokesman said "at this stage" they were not concerned about running dry, although some supermarkets have brought back caps on toilet roll caps.

While strikes are not uncommon in New Zealand, lockouts are rare.

Mr Phillips said he was severely concerned for his workforce, without pay for three weeks after Essity's action.

Workers are seeking wage increases that match inflation, and Essity has offered three per cent increases over the next three years and a sign-on bonus.

"They've never come off three per cent," Mr Phillips said of negotiations, "and if we accept we're going backwards."

"One of the most frustrating bits about this negotiations is the big managers are in Australia. The local managers have no say; it's all been driven from Australia."

General manager Peter Hockley said Essity's offer was "more than fair and reasonable" and the lockout came after fruitless talks and strikes.

Essity has also put off a $NZ15million ($A13.35million) upgrade.

The dispute worsened this week when Essity moved to block workers from making financial hardship withdrawals from their superannuation accounts.

In Auckland, Kiwi workers are striking at two Visy-owned manufacturing plants for the first time in 25 years.

Workers are seeking a one-off 10 per cent increase and streamlined overtime arrangement, as their current deal incentivising long hours before overtime provisions kick in.

"We have kids, and we don't see them, only in the mornings before they leave for school or at weekends," union delegate Reaaz Ali said, who said he worked six-day weeks with 12-hour shifts.

"We feel we don't have a choice, and it's killing our health as well."

E tu union leader Jen Natoli said the the strikes came after Visy's offer produced an average increase that would be a wage cut in real terms.

Visy did not respond to requests for comment.

Australian Associated Press