According to the AP, Thai Union exports thousands of cans of cat food products including Fancy Feast, Meow Mix and Iams.
Fancy Feast - one of Swiss food giant Nestle's brands - and Iams products are widely sold in New Zealand.
Antoinette Laird, corporate public relations director for Pak'nSave and New World operator Foodstuffs, said the company was taking the issue seriously.
"Foodstuffs in no way, shape or form has ever or will ever knowingly stock a product that is the result of illegal business practices or slave labour," Ms Laird said. "With regard to Nestle and its Fancy Feast products stocked in our stores, we are aware that Nestle are working through their supply chain to identify any potential unlawful practices."
A spokeswoman for Countdown, which also stocks Fancy Feast, said the allegations were obviously serious and the supermarket operator was speaking with Nestle to better understand the situation.
Nestle Oceania spokeswoman Margaret Stuart said the practices uncovered by the AP were completely unacceptable.
"We are engaging with our seafood suppliers in Thailand to identify any potential unlawful labour practices and pursue appropriate actions to eliminate such practices from our supply chain," Ms Stuart said. "To this end, our main seafood supplier in Thailand has begun working with an independent consulting firm to trace products through the different tiers of its supply chain to the ports of origin in Southeast Asia."
A local spokeswoman for Mars, which owns the Iams brand, said the company did not tolerate forced labour and had contacted its Thailand-based fish processors in order to establish "greater transparency in their sourcing".
AP reported yesterday that Thai Union had cut its ties with the supplier found by the investigation to be connected with slavery.
High sea slavery
• Associated Press investigation found widespread slavery in Indonesia's fishing industry.
• Slave-caught fish was allegedly supplied to a Thailand-based firm that manufactures product for pet food brands including Fancy Feast and Iams.