South Carolina regulators on Tuesday rejected an effort by the Trump Organization to limit its environmental cleanup liabilities at an industrial site once owned by President Trump’s eldest son.

The decision is a rebuke of the Trump Organization and could result in millions of dollars in added costs for the company. It followed a refusal by the organization to provide regulators with required information about business and financial relationships between the president and his son Donald Trump Jr.

The Trump Organization had no immediate comment.

The issue grew out of the younger Mr. Trump’s involvement in Titan Atlas Manufacturing, a company that he helped start in 2010 in North Charleston, S.C., and that failed two years later.

In 2014, Donald J. Trump, while he was still running the Trump Organization, bailed out his son, who was then facing payment of a $3.65 million bank loan to Titan Atlas. The elder Mr. Trump created an entity called D B Pace, which took over the loan and the six-acre Titan Atlas site.