One of the two indicted associates of President Trump’s personal lawyer, Rudolph W. Giuliani, on Wednesday tied the case to the president himself, saying that some of the evidence gathered in the campaign-finance investigation could be subject to executive privilege.

The unusual argument was raised by a defense lawyer in federal court in Manhattan as the two associates, Lev Parnas and Igor Fruman, pleaded not guilty to federal charges that they had made illegal campaign contributions to political candidates in the United States in exchange for potential influence.

Mr. Parnas and Mr. Fruman have become unexpected figures in the events at the heart of the House Democrats’ impeachment inquiry, having played a role in helping Mr. Giuliani’s efforts on behalf of President Trump to dig up information in Ukraine that could damage former Vice President Joseph R. Biden Jr., a prospective Democratic challenger.

Mr. Giuliani has denied wrongdoing but has acknowledged that he and the two men worked with officials in Ukraine to collect damaging information about the American ambassador to Ukraine and other targets of Mr. Trump and his allies, including Mr. Biden and his younger son, Hunter.