The company has said its offer to workers is fair.
Pulp and Paper Union Kawerau secretary Tane Phillips said union members were in facilitation with Essity negotiators yesterday and today.
Phillips said it was "a bit early to tell" how the negotiations were going. "We're trying our best to make headway ... to get to an agreement."
In a written statement, Essity said it was in "facilitated bargaining" for two days and would not comment further at this time.
A Bay of Plenty New World manager said it was "light" on some toilet paper products and some shelves were empty on Wednesday.
"But we can get enough toilet paper and that's not a problem for us."
The manager said the Essity mill worker lockout meant the less than expected had been supplied.
Asked how this was affecting customers, the manager said there were still options.
"We have got enough cover to cater for almost every customer's needs."
A Foodstuffs spokesperson said it had been working closely with Essity and other supplier partners to ensure it had enough toilet paper to go around.
"If customers continue to shop normally we're in a good position to ensure there's plenty of stock for customers."
A Countdown spokesperson said it was working closely with toilet paper supply partners to ensure there was plenty of stock available for everyone.
"As long as everyone shops as they normally would, we have no concerns about a possible shortage of toilet paper."