NEWARK, N.J. — The judge in the bribery trial of U.S. Sen. Bob Menendez and a wealthy friend delayed ruling Wednesday on whether to grant the defense’s motion to dismiss the charges against them, but in doing so he appeared to indicate he has doubts about a legal concept at the heart of the government’s case.

During more than three hours of arguments from both sides after the prosecution rested, U.S. District Judge William Walls expressed reservations that prosecutors have shown direct links between alleged bribes by Florida eye doctor Salomon Melgen and meetings and other interactions Menendez, a New Jersey Democrat, had with government officials, allegedly to advance Melgen’s business interests.

The indictment alleges Melgen plied Menendez, his longtime friend, over several years with gifts that included free flights to the Dominican Republic on his private jet and stays at luxury hotels.

Prosecutors allege those were bribes under what is known as the stream of benefits theory, in which Melgen essentially kept Menendez on retainer and asked him for favors “as opportunities arose,” according to the indictment.

Defense attorneys have argued that a 2016 U.S. Supreme Court ruling that reversed the conviction of former Republican Virginia Gov. Bob McDonnell invalidated the stream of benefits theory, a claim prosecutors have denied.

The trial judge focused on the question Wednesday, asking Department of Justice attorney Peter Koski, “What’s the quid for those quos?” referring to the Latin quid pro quo, or “something for something.”

“I’m trying to find out how you link the quid to the alleged quo and vice versa,” the judge went on, adding, “I know what you’re trying to do, but I don’t think you can do it.”

If the judge rules the stream of benefits theory can’t be applied to this case, it could cut out the heart of the 18-count indictment: the 12 bribery counts, six against each man; the top count, conspiracy to engage in honest services wire fraud, and possibly three others.

The judge indicated he would leave intact one count of making false statements against Menendez for not declaring Melgen’s gifts on his Senate disclosure forms.

The other central issue raised by the Supreme Court’s McDonnell decision — what is considered an official act by a public official? — was expected to dominate the arguments on Menendez’s motion to dismiss. But the judge all but told attorneys he considered Menendez’s actions to fall under that definition.

When attorney Abbe Lowell, representing Menendez, noted that Menendez had no power to compel the executive branch officials he met with to act on Melgen’s behalf, the judge responded, “The Supreme Court is not naive collectively, and I don’t believe your last point would sit well with them. Anyone with a dollop of political experience knows that an entreaty or request from one member of the legislative branch to another member of the executive branch … would have an effect.”

The parties are scheduled to reconvene Monday, and both sides may submit briefs to the judge augmenting their oral arguments before then.