BRUSSELS — Carbon trading put the European Union in the environmental vanguard.

Since 2005, the trade bloc has operated the world’s only continentwide system that puts a cap on greenhouse gas emissions and that requires major polluters to hold tradable allowances.

But the system has also been the most “costly climate policy program in the world,” according to Jürgen R. Thumann, the president of BusinessEurope, a powerful confederation of industry and employer groups.

Mr. Thumann said European business leaders are desperate to expand the system to the United States and eventually across the globe to reduce the “dangers to our ability to compete internationally.”

But with talks on a new global climate treaty seemingly at a stalemate, and with climate legislation delayed in major polluting countries like the United States and Australia, those prospects look increasingly distant.