WILMINGTON, Del. — Jurors in the Hunter Biden federal gun trial began deliberating Monday afternoon after prosecutors and defense attorneys made their final pitches in the first criminal case against a child of a sitting president.

The jury of six men and six women in Wilmington did not reach a verdict in an hour of deliberations after listening to both sides finish their closing arguments.

They will resume deliberations on Tuesday morning.

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Mr. Biden faces three felony charges arising from his purchase of a handgun in October 2018. Prosecutors have charged him with illegally possessing a gun as a drug user and lying about his addiction to crack cocaine at the time of the purchase.

If convicted on all counts, he faces a maximum of 25 years in prison. As a first offender, he would likely receive little, if any, prison time.

Closing arguments began Monday afternoon after Mr. Biden’s team rested its case. Mr. Biden declined to testify in his defense. Both sides took more than an hour to lay out their arguments to the jurors.

Prosecutor Derek Hines suggested that Mr. Biden bought the gun for protection during drug deals. He quoted a passage in Mr. Biden’s book in which the defendant wrote about having guns shoved in his face while trying to buy crack.

Mr. Hines said if the trial evidence doesn’t show that Mr. Biden was a crack addict in 2018 when he bought the gun, “then no one is a crack addict.”

Earlier, prosecutor Leo Wise connected a series of text messages sent by Mr. Biden, witness testimony and the defendant’s own words in his memoir to show that President Biden’s son was deep into his crack addiction when he bought the firearm.

In his 90-minute closing argument, Hunter Biden’s attorney Abbe Lowell compared the government’s case to a magician’s trick. He said the case was nothing more than “suspicion or conjecture.”

“It’s time to end this case,” he told the jury.

Mr. Lowell argued that Mr. Biden didn’t believe he was an addict when he filled out the federal form to purchase a firearm because he wasn’t actively using drugs at the time.

He said none of the prosecution’s witnesses had seen Hunter Biden use drugs in October 2018, when he bought the firearm, or during the 11 days he possessed it.

Mr. Lowell told the court that prosecutors didn’t prove that Mr. Biden’s repeated withdrawals of cash were used for drug purchases, nor did they connect to him the remnants of crack cocaine found in a leather pouch he owned.

“Proof beyond a reasonable doubt is not suspicion or conjecture and hoping you won’t realize the difference,” he said.

During his argument, Mr. Wise urged jurors not to leave behind their common sense. He pointed to text messages in which Mr. Biden told his ex-girlfriend and sister-in-law Hallie Biden that he was smoking crack two days after the gun purchase and that was his “truth.”

Defense attorneys argued that he was simply trying to avoid being with her.

Mr. Wise said jurors should “take the defendant’s word for it. That’s his truth.”

The prosecutor said nothing supported the defense’s suggestion that Hunter Biden was withdrawing large sums of money for rehabilitation or other purchases because financial statements show rehabilitation payments were made with a credit card.

Mr. Wise also referred to a text message between Mr. Biden and his daughter Naomi during an October 2018 trip to New York. In the text, Mr. Biden asks whether her boyfriend could meet him around 2:45 a.m. to exchange cars.

“I’m really sorry Dad, I can’t take this,” she responded.

Members of Hunter Biden’s famous family were in the courtroom, including first lady Jill Biden, President Biden’s brother James Biden, the president’s sister Valerie Owens and Hunter Biden’s half sister Ashley Biden.

Near the start of his argument, Mr. Wise gestured to the Biden family sitting in the crowd.

“All of this is not evidence,” Mr. Wise said. “The people sitting in the gallery are not evidence. You may recognize some of them from the news or the community. … Respectfully, none of that matters,” he said.

He received a sharp rebuke from Mr. Lowell. When he began his closing argument, Mr. Lowell said the prosecution shouldn’t have referred to the defendant’s relatives in the courtroom.

He countered that Hunter Biden’s famous last name doesn’t change the fact that he is presumed innocent until proven guilty.