Over nearly 60 years and two generations, Chatchai Lertviwatkul’s family business in Thailand was transformed from a manufacturer of leather gloves to a producer of pet food and treats, with a third of its products shipped to the United States from a modest factory on the outskirts of Bangkok.

So when Mr. Lertviwatkul learned in April that President Trump wanted to impose a 36 percent tariff on goods from Thailand, he was stunned. What would that mean for his company, S.I.P. Siam Inter Pacific, and the country’s pet food export industry?

After a decade of rapid growth, Thailand is now the biggest overseas supplier of pet food to the United States, accounting for more than one-third of all imported cat and dog food.

As Thailand and dozens of other countries near the end of a 90-day rollback of punishing tariffs to negotiate a permanent deal, Mr. Lertviwatkul, 52, said the shock had worn off, but the future of the company’s American business remained unclear.

“We need to see how the Thai government will negotiate,” he said, speaking above the hum of a factory churning out lickable cat treats for a Canadian customer and mint-flavored dog snacks in the shape of a toothbrush. “We need to wait and see,” he added. “There’s nothing much we can do.”