“We should all care, because that cost will have to be passed on, in the form of higher prices for products sold to consumers or a lower return for investors,” said Kenneth E. Bentsen Jr., a former House lawmaker turned financial industry lobbyist, whose organization Sifma has urged Mr. Gensler to compromise on the cross-border rules.

Some of the strongest objections have come from foreign regulators, including officials from Britain, Russia, Japan and Germany, who complained about the plan last month in a letter to Treasury Secretary Jacob J. Lew. Global markets, they said, “will not be able to function under such burdensome regulatory conditions,” advocating instead that the United States agree to respect rules each nation adopts, assuming they are reasonably compatible.

Mary L. Schapiro, who recently stepped down as chairwoman of the Securities and Exchange Commission, said she admired Mr. Gensler for his doggedness. But, she noted, “he believes very strongly in the positions he takes — that does not always lend itself to compromise quickly.”

The S.E.C., which has jurisdiction over a much smaller share of derivatives trading than Mr. Gensler’s agency, is scheduled to consider a narrower cross-border requirement on Wednesday. With American regulators in disagreement, the industry could have more leverage.

The role of Mr. Gensler’s agency greatly expanded under Dodd-Frank, which called for significantly tighter regulation of derivatives, used by a broad array of companies to help manage risk. An airline, for instance, uses them to hedge against the fluctuating cost of jet fuel. One form of derivatives, credit-default swaps, helped topple the giant insurer American International Group in 2008, deepening the financial crisis.

In the fight over the law’s provisions, the commission has been outmatched, said Bart Chilton, one of three Democratic appointees on the panel. “They have really unlimited resources,” he said of industry officials. Rules expected to take one year in the making have stretched out to three.

“It has created what I call dysfunction junction,” he added.

Bank of America, Citigroup and JPMorgan Chase were among the first to weigh in. Kenneth M. Raisler, a former general counsel at the commodity commission and now a partner at the New York-based law firm Sullivan & Cromwell, said the plan would damage his clients in overseas markets, as foreign customers would start to avoid American banks. JPMorgan Chase alone had $70 trillion of derivatives outstanding at the end of last year, a large portion of which were booked overseas.