“I’m embarrassed about how people think about New Jersey based on Senator Menendez’s behavior,” he said. “It’s embarrassing. He must be and he will be held accountable by the voters this November.”

Political advisers to Mr. Menendez said the senator would not comment on Mr. Hugin’s remarks.

Mr. Menendez is emerging from a monthslong politically damaging corruption trial that ended in a mistrial after a jury was unable to reach a verdict. After saying they were going to retry Mr. Menendez, federal prosecutors reversed course after a federal judge acquitted him of several of the charges.

Mr. Menendez, who has not formally declared his candidacy but has given every indication that he plans to run again, has a $4.1 million campaign fund and is unlikely to face a serious challenge in the Democratic primary, having locked up nearly every key Democratic endorsement in the state.

Mr. Hugin, a U.S. Marine veteran who was born in Union City, just like Mr. Menendez, pledged that he was a “fiscal conservative,” but would not be beholden to the Republican Party on issues that hurt New Jersey, like capping state and local tax deductions under the new tax law.

“If President Trump or any other Republican has an idea or a view that is bad for New Jersey, I will forcefully stand up and disagree with them,” he said.