A luxury Mercedes-Benz, gold bars, exercise equipment and stacks of cash featured prominently in a federal indictment that charged Senator Robert Menendez with accepting a sordid array of bribes.

Now, prosecutors say a diamond engagement ring for the senator’s future wife, Nadine Menendez, was also part of the elaborate bribery scheme — and a source of infighting between co-defendants who are expected to stand trial together in May.

Wael Hana, a longtime friend of Ms. Menendez’s who is also charged in the alleged conspiracy, attempted to cheat her out of the full value of the ring, according to court documents filed late Monday by prosecutors in Manhattan.

In doing so, Mr. Hana, an Egyptian-American businessman who founded a halal meat company that prosecutors say was used to funnel bribes to the Menendezes, threatened to derail plans for the senator to assist the government of Egypt — part of the complicated plot he is accused of.

“[Hana] was about to ruin things with Bob,” a confidential source, who was in touch with Egyptian officials, said, according to the government’s filing. “Bob who is starting to listen to us.”

Mr. Menendez, a Democrat from New Jersey, has pleaded not guilty, as have Ms. Menendez, Mr. Hana and two other defendants.