The veteran Prince William County prosecutors were relentless.

In their closing arguments Tuesday, they urged jurors to give Ronald Hamilton, a former Pentagon information-technology specialist who killed his wife and a rookie police officer, the death sentence instead of life in prison without parole. Again and again, they reminded jurors of the harrowing sequence of events that played out Feb. 27, 2016, at Hamilton’s home in Woodbridge, Va.: First, the Army staff sergeant shot 29-year-old Crystal Hamilton with a handgun four times after they had gotten into a fight and she called 911. Then he grabbed his AK-47 and shot three Prince William police officers, injuring two and killing Ashley Guindon, who was working her first shift.

“He shot [his wife] in the face, shot her again as she’s going down to the floor, then shot her again in the brain stem,” said Richard A. Conway, chief deputy assistant commonwealth’s attorney. When police arrived, Conway said, Hamilton made a premeditated decision to use a semiautomatic assault weapon, thinking, “ ‘This .45 is not going to do it. [The police] are all wearing ballistic vests, and the .45 won’t go through that.’ ”

“He richly deserves the ultimate punishment,” Conway said.

Prosecutor Matthew B. Lowery was unsparing. “Put him in the grave,” he told the jury, “because that’s where he belongs after what he’s done.”

The jury of 10 women and two men began deliberating Tuesday but did not reach a verdict. On Wednesday they will resume considering what sentence to impose.

On the final day of Hamilton’s capital murder trial, defense attorneys and prosecutors tussled over one idea: Who gets mercy? Does a man who killed two people, one of them a police officer, deserve life in a maximum-security prison without any chance of getting out? Or should that man face execution?

The Prince William prosecution team has pushed for — and won — numerous death sentences in the past several decades, including the execution of Washington sniper John Allen Muhammad. They argued that Hamilton, convicted last month of capital murder, deserves no compassion.

Giving him the death sentence would send a message to other would-be killers of police that the county has no tolerance for the murder of its law enforcement officers. He needs to die, they said, because his repeated shooting of his helpless wife — while their then-11-year-old son was in the house — was excessive and “depraved.”

Defense attorney Ed Ungvarsky spent two hours trying to convince the jury that Hamilton, given his military career and two deployments to Iraq, was worth sparing.

“Mercy isn’t earned. It’s given,” Ungvarsky said, adding that giving Hamilton life in prison without parole would still be extremely harsh. “Mercy is everywhere in this room. You should consider mercy.”

He said Hamilton, whose father is a retired second-in-command of the Charleston, S.C., police department, should not be put to death like “some diseased animal.” He cited aphorisms by William Shakespeare, the author Richard Wright and Coretta Scott King to make the case that Hamilton should live and that his murders won’t be “redeemed by an act of retaliation.”

He cited evidence that Hamilton had once saved a colleague’s life in the war zone after they had come under a mortar attack, that he had grown up without a steady father figure, and that after his Iraq deployments, he probably had undiagnosed post-traumatic stress disorder.

At one point, Ungvarsky began showing the jury photos of Hamilton as a child or in other happier moments. “If you kill this man, you kill this child, too,” he said, flashing a picture of the defendant as a boy.

He also said Hamilton has been struggling with mental issues for years, dating to his childhood when he wrote a suicide note to his mother that she was supposed to find after he had killed himself. “Dear Mom, the reason I killed myself was because my life wasn’t straight,” he had written. “PLEASE don’t let this letter be in the news.”

“If you kill this man, you kill the boy who wrote this letter,” Ungvarsky said.

In the end, Hamilton’s defense attorney said his crimes were far less malicious than those of other more-notorious people who have avoided the death penalty, including Zacarias Moussaoui, a conspirator in the 9/11 attacks, and Unabomber Ted Kaczynski.

“If you see the humanity in him, even a speck, you must give a life sentence,” Ungvarsky told jurors.

As Ungvarsky and the prosecutors went back and forth, Hamilton mostly kept his face in his hands, at one point blowing his nose. One attorney sitting next to him kept patting his upper back and talking into his ear.

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