According to Unite, a 250,000-member labour group representing US textile workers, H&M is guilty of not allowing workers to organise.
However, H&M investor relations manager Clas-Henric Enhorning said the high street giant was "not anti-union", despite Unite's call for a 'card count' among staff that would make a union agreement mandatory if 50 per cent of workers had signed up for union cards.
"If half of the workers in the United States want a union agreement, we will make one," Enhorning said.
He added that a secret vote, which could be arranged at the request of 25 per cent of workers, was more preferable for H&M.
Meanwhile, Unite spokesman Scott Zdrazil said the group was "continuing to mobilise other union activists' support" against the retailer.
"As H&M expands in the United States, the actions and protests continue," he said.
"We want negotiations now, and concrete results."
So far, protests have included the placement of a giant plastic skunk outside the H&M store on Manhattan's 5th Avenue, one of the world's busiest shopping strips.
Despite the lengths Unite has gone to, Enhorning claimed H&M had not seen a negative sales impact from the protests.
"These kinds of events happen quite often in the US, and the customers don't seem to care that much," he said.
Swedish H&M has operated in the US since 2000.