Seamstresses in Bangkok and Manila have been protesting before Swiss embassies to air complaints against the Aargau-based lingerie firm, Triumph International.
The company, with headquarters in Zurzach, said it would make 3,714 workers redundant at sister firms in Thailand and the Philippines.
Triumph, which employs 40,000 people worldwide, said in a statement that a "general downturn in consumer demand" prompted the move. It said it had given written notices to employees according to law and that discussions were still underway with unions over severance pay.
"The company deeply regrets that any job losses are necessary," the statement said. "Triumph is making every possible effort to ensure that all affected employees are being treated fairly and with respect."
But the Berne Declaration, a group that strives for equitable North-South relations, and Unia, a Swiss trade union, are backing the workers. They also say a former Triumph supplier fired workers earlier this year without payments for outstanding wages or severance pay.
"It is conspicuous that only factories with well organised unions are affected," the Berne Declaration and Unia said in a statement.
The groups are demanding that Triumph revoke the dismissals and work with unions on a planned restructuring to ensure international guidelines are met.
Workers were informed of the cuts in late June. After weeks of picketing in front of the factories, the workers are now taking their protests before Swiss embassies in Thailand and the Philippines to raise awareness about their plight.
In compliance with the JTI standards