Alex Wilks, campaign director of Avaaz, which has 21 million members worldwide, said its online petition was aimed at the chief executives of Gap and H&M. The petition says, “Your companies and other multinationals profit from cheap labor, and can do much more to reduce the dangers of the places where your products are made.” Bangladesh, the world’s second-largest apparel exporter after China, has the lowest minimum wage in the world — $37 a month — which has helped it attract billions of dollars in orders from the West.

“We feel that H&M and Gap are well placed to turn what have become death traps into safe factories,” Mr. Wilks said. “We’re targeting these two companies because they’ve made commitments to ethics, and we feel that this leadership makes them well placed to not only lead their own companies but also to lead the rest of the industry to sign up to these strong and enforceable agreements.”

Two weeks ago, the German government sponsored a conference of retailers, apparel brands and antisweatshop groups that sought to push the companies to agree to take strong safety measures in Bangladesh. The antisweatshop groups have set Wednesday, May 15, as a deadline to persuade retailers to join the PVH-Tchibo plan, and they say that any retailers that do not sign will be the target of new protests.

Saying that his company has a strong reputation on social responsibility, Bill Chandler, a Gap spokesman, insisted that the attacks against his company were misplaced. “It’s perplexing that they’re targeting us when we’re a leader in taking action on the ground while many others are passively sitting on the sidelines,” he said.

Gap has hired a respected fire safety expert to inspect the dozens of factories it uses in Bangladesh. Gap has also said it will spend $22 million for fire safety improvement there.

H&M, in a statement, said that improving fire and building safety in Bangladesh was one of its priorities. “We are working at full speed to reach the best solution with other stakeholders,” the company said.

Mr. Liu has been singling out Walmart in particular. “The tragedy in Bangladesh may finally bring home the lesson to Walmart and others that they are responsible for their suppliers,” he said. Walmart, Gap and H&M did not use any of the five factories in the building that collapsed, but customs records show that two American companies — the Children’s Place and Cato Fashions — bought significant amounts of apparel from factories there over the last year.