The criminal case against two associates of President Trump’s private lawyer, Rudolph W. Giuliani, became explicitly connected to the president on Wednesday when a defense lawyer made a surprising argument that some of the evidence gathered in the investigation could be subject to executive privilege.

The two men, Lev Parnas and Igor Fruman, were arrested and accused of making illegal political campaign contributions in exchange for influence. The indictment filed by federal prosecutors did not name or identify Mr. Giuliani or Mr. Trump in connection with the charges.

But Mr. Parnas and Mr. Fruman have been linked to Mr. Giuliani’s attempts on behalf of Mr. Trump to gather damaging information in Ukraine about the president’s political foes. That campaign is the focus of House Democrats’ impeachment inquiry into Mr. Trump.

The executive privilege argument given on Wednesday drew renewed attention to the work Mr. Parnas and Mr. Fruman conducted to benefit Mr. Trump, as well as to the ties between the two men, the president and Mr. Giuliani.