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.

Lawyers for the senator did not immediately respond to a request for comment, and his wife’s lawyers had no comment. Mr. Hana’s lawyer, Lawrence S. Lustberg, had no comment, except to say he would be responding to the government’s filing in court papers due Monday.

Nicholas Biase, a spokesman for the U.S. attorney’s office in the Southern District of New York, where the defendants have been charged, also declined to comment.

The new filing comes in response to the senator’s request to suppress evidence seized during searches of the house he shares with Ms. Menendez in Englewood Cliffs, N.J. The senator’s lawyers have said that warrants permitting the searches were overly broad and ignored evidence favorable to Mr. Menendez.

But in justifying the need for the warrants, prosecutors from the Southern District of New York offered a trove of new details about the alleged bribery plot itself.

There are snippets from secretly recorded conversations and details about where investigators found two bags filled with roughly $100,000 in cash each. (“In the basement of Menendez and Nadine Menendez’s residence, on top of a large rack of clothes hangers,” prosecutors wrote, adding, “Under the jackets were four boots, stuffed with cash, including one boot containing in excess of $5,000 in $50 bills.”)

As part of the bribery plot, prosecutors said Mr. Hana arranged for carpet installation at Ms. Menendez’s home. And at times, the senator placed calls to what the couple referred to as Ms. Menendez’s “007” phone — “an apparent reference to the fictional character James Bond,” prosecutors wrote.

But perhaps the most unusual new detail in the filing involves an element of the lengthy federal investigation that did not appear to factor into any of the three successive indictments against Mr. Menendez, Ms. Menendez and three New Jersey businessmen.

Prosecutors noted that Mr. Menendez contacted mayors in New Jersey during the pandemic, in late 2020 and early 2021, to ask them to authorize use of a specific laboratory — which at the time was paying Ms. Menendez — to perform Covid-19 testing.

Taken together, prosecutors said, these details amount to “substantial evidence that Menendez did in fact know about the corrupt quid pro quo.”

The engagement ring, according to prosecutors, was given to Nadine Menendez as part of a $150,000 bribe from a man who had enlisted Mr. Menendez’s help to avoid criminal penalties after being charged with insurance fraud in New Jersey.

Part of the money went toward a new Mercedes-Benz convertible for Ms. Menendez, prosecutors said.

The new car replaced a vehicle that police records show Ms. Menendez was driving in December 2018 when she struck and killed a pedestrian, Richard Koop, in Bogota, N.J. Ms. Menendez was not tested for drugs or alcohol and was not charged with wrongdoing. The New Jersey attorney general’s office has said it was reviewing the crash investigation, but has refused to respond to questions about the status of the inquiry.

Roughly $35,000 of the $150,000 bribe was intended to cover the purchase of a diamond ring, according to prosecutors.

But the ring Mr. Hana bought cost only $12,000. He used the excess funds to buy two watches, a bracelet and a necklace for himself, yet had the jeweler provide a receipt indicating that the ring he gave Ms. Menendez cost $35,000, prosecutors said.

“The Hana associate also explained that Menendez knew that Hana shortchanged him with respect to the ring, and that Nadine Menendez (the ‘gander’) had taken the ring back to the jeweler and learned that it was worth less money,” the court filing noted, citing a code name used for Ms. Menendez.

In their filing on Monday, the Southern District prosecutors also responded sharply to an assertion by Mr. Menendez’s lawyers that the case stemmed from “the government’s apparent zeal to ‘get back’ at Senator Menendez” for his avoiding conviction in a 2017 federal corruption trial in New Jersey that ended in a hung jury and dismissal of charges against him.

The prosecutors, noting that the senator’s earlier case involved different facts, a different co-defendant and a different prosecution team, called the accusation “patently false.”

The prosecutors also contradicted a claim by Mr. Menendez in a sworn declaration that accused the F.B.I., which searched his house in June 2022, of leaving the home “in complete disarray.” Interior doors had been forcibly broken down, furniture had been haphazardly moved around, and filing cabinets, desk drawers, dressers and closets had all been rummaged through and their contents strewn about, Mr. Menendez wrote.

Prosecutors, calling the senator’s claim “at best, hyperbolic,” said that although physical searches require the movement of some objects, time-stamped entry and exit photographs taken by the F.B.I.’s search team “show that the house was in substantially similar condition at the end of the search as it was in the beginning.”