U.S. Rep. Michael Grimm, center, and Democratic challenger Domenic Recchia with moderator Diana Williams before a debate on Friday at WABC-TV; the debate will be aired by the station at 11 a.m. Sunday. The men are vying to represent the 11th Congressional District. Associated Press

U.S. Rep. Michael Grimm and his Democratic challenger, Domenic Recchia, engaged in a fiery debate on Friday, facing off over everything from the Rev. Al Sharpton to the federal indictment at the center of the Staten Island race.

The gloves came off moments into the debate, and at times the two men seemed as though they may come to blows.

Mr. Grimm, a Republican, sat wide-eyed as Mr. Recchia repeatedly reminded the audience of his opponent’s tax-fraud charges. Mr. Recchia said Mr. Grimm should resign.

“You lied to the FBI. You lied to the U.S. attorney’s office,” Mr. Recchia said, waving his finger in Mr. Grimm’s face.

Sitting ramrod straight, Mr. Grimm, who has said he is innocent, said it was Mr. Recchia who was lying.

“I’ve never even been interviewed by the FBI. I’ve never been interviewed by the U.S. attorney,” he shot back. “So how could I lie to them?”

In response, Mr. Recchia let out a sigh.

“You are facing a 20-count indictment. This is ridiculous!” he said.

The debate was held in the Upper West Side studio of WABC-TV and will be aired by the station at 11 a.m. Sunday.

The candidates often interrupted each other, shaking their heads and rolling their eyes. At times, moderator Diana Williams, had to intervene.

“Gentlemen!” Ms. Williams said at one point.

Asked whether he would be effective with an indictment hanging over his head, Mr. Grimm said he would resign if found guilty. He said he had a right to a day in court, something he said he fought for personally as a Marine.

“That’s part of our constitutional rights—one I put the uniform on to defend, which I’m very proud of,” said Mr. Grimm, who served in the Gulf War.

Mr. Recchia accused Mr. Grimm of lying about his role in passing flood insurance legislation, known as the Biggert-Waters Act, popular with Staten Islanders. But his attack backfired when he appeared not to know the name of the law.

“What’s the name of that bill?” Ms. Williams asked him.

“The-the bill that would lower premiums, OK?” Mr. Recchia replied.

Another awkward exchange came as Mr. Grimm asked Mr. Recchia if he knew how much money was included in a package of federal Sandy aid.

“You tell me since you know so much,” Mr. Recchia snapped, as Mr. Grimm laughed, bouncing a little in his seat.

Substantive issues took a back seat during sometimes bitter exchanges.

When Messrs. Recchia and Grimm were asked about the death of Eric Garner, an unarmed man who died after being subjected to an apparent police chokehold, both said they had confidence in Staten Island District Attorney Daniel Donovan.

“Out of respect to the Garner family and to the NYPD, I’m going to reserve a decision until the district attorney finishes his full investigation,” Mr. Recchia said.

Mr. Grimm called the death a tragedy but said he supported Mr. Donovan as well. He also took the opportunity to criticize Mayor Bill de Blasio for allowing the Rev. Al Sharpton to become involved.

“I think the mayor made a very big mistake by bringing Al Sharpton to center stage,” he said. Mr. Grimm added that he thinks relations between police and communities on Staten Island are “pretty good.”

As the debate came to a close, Mr. Recchia told voters Mr. Grimm was unfit for office. “This district has not been represented by someone who they can be proud of,” he said. “In addition to that, he threatened to throw a reporter off a balcony,” Mr. Recchia added, referring to a January incident in which Mr. Grimm was heard on camera threatening to throw a reporter off the balcony of the U.S. Capitol Building. He has since apologized.

Mr. Grimm said his constituents know and trust him. “They know me,” he said. “They know my heart and who I am as a person.”

Write to Mara Gay at mara.gay@wsj.com