Exxon and the Treasury Department discussed the situation directly in 2015, but according to Exxon it heard nothing more for a year. Then last year, Treasury indicated that the comments made by White House and Treasury officials in the press did not give Exxon the go-ahead. Instead, the department pointed to guidance on its website that warned companies to be cautious about entering into contracts with people who were under sanction.

Believing that it had followed the guidance it was given, Exxon declined to concede it had violated the sanctions and submit to a penalty.

“The issue is will the U.S. Department of Justice defend a position by an agency that you shouldn’t listen to what the White House says?” said Alan T. Jeffers, an Exxon spokesman. “We feel very strongly that what they’ve chosen to do is contrary to the law.”

For its part, the Treasury Department has been silent on the matter beyond a three-page enforcement document issued on Thursday stating that Exxon’s “senior-most executives” knew of Mr. Sechin’s status when Exxon engaged in behavior that caused “significant harm” to the sanctions program.

The department would not say if Mr. Mnuchin was involved in the final decision, and Mr. Tillerson’s aides maintain that he was unaware because he had recused himself from matters related to Exxon.

“You have to wonder how far up the chain at the Treasury Department this went,” said Thad McBride, an international trade lawyer at Bass, Berry & Sims, noting that the pointed language about high-level knowledge appeared to be directed at Mr. Tillerson. “It is extremely unusual that Treasury would do that.”

The State and Treasury Departments typically coordinate closely on sanctions. At the State Department, an Office of Economic Sanctions Policy advises Treasury officials on foreign policy. The agencies often announce new sanctions in tandem.