Federal prosecutors in New York announced on Wednesday the filing of a new indictment that charges a former Turkish economy minister and three other Turks with participating in a broad conspiracy to violate the United States’ sanctions against Iran.

The new charges represent a significant expansion of a case that had already drawn the attention of the Turkish president, Recep Tayyip Erdogan, senior members of the Trump administration and President Trump’s informal adviser, Rudolph W. Giuliani.

Mr. Giuliani has been retained by one defendant, Reza Zarrab, to try to negotiate a diplomatic resolution to his case. Mr. Giuliani has met with Mr. Erdogan to discuss the case; in the past, Mr. Erdogan claimed there were “malicious” intentions behind Mr. Zarrab’s prosecution.

Prosecutors have charged that Mr. Zarrab, a gold trader and dual citizen of Iran and Turkey, and his co-defendants conspired to facilitate millions of dollars in transactions on behalf of Iran and other sanctioned entities through the use of front companies and false documentation.