A federal jury in Massachusetts agreed Monday to condemn admitted serial killer Gary Lee Sampson to death, recommending handing out the ultimate punishment for a weeklong crime spree that left three people dead in two states in July 2001.

It was the second time a jury had voted to give Sampson the death penalty. The initial sentence was in 2003, and came more than a half-century after Massachusetts last executed someone. It was later overturned, prompting the just-concluded retrial.

The new jury of seven men and five women also favored sending Sampson to his death for carjacking and killing Jonathan Rizzo, a 19-year-old college student from Kingston. The teen had offered to give Sampson a ride after getting out of a work on a Friday night.

However, the jury could not come to a unanimous decision on a sentence for the killing of Philip McCloskey, a 69-year-old plumber from Taunton who had also given Sampson a ride. Sampson will receive a sentence of life in prison without the possibility of parole for that crime.

The 2003 jury had agreed to sentence Sampson to death for killing both McCloskey and Rizzo. That verdict was overturned because one of the jurors lied during selection.

“Today, the jury has spoken,’’ US Attorney Carmen M. Ortiz said at a news conference. “Gary Lee Sampson will pay with his life for all of the heinous crimes he committed,’’ she said, choking up as she embraced the relatives of Sampson’s victims. “He blamed everyone but himself for his life of crime, and today a jury decided for the second time that he will pay the ultimate price.’’

The jury deliberated for roughly 16 hours over three days before reaching its verdict. The 2003 jury deliberated for 11 hours.

Mary Rizzo, Jonathan’s mother, a consistent presence at the trial who told jurors how the killings had irreparably damaged her family, thanked jurors for the decision.

“This has been so brutal, I’m so glad it’s over,’’ she said.

US Magistrate Judge Leo T. Sorokin said he would schedule Sampson’s official sentencing hearing at a later date. Though the jury recommended death, only a judge can officially impose a sentence. But Sorokin is bound by the jury’s decision.

Sampson’s sentence is the second time in less than two years that a federal jury has agreed to hand out a death sentence in Massachusetts, which does not allow capital punishment in state court.

In May 2015, a jury agreed to sentence Boston Marathon bomber Dzhokhar Tsarnaev to death. He has appealed.

State courts in Massachusetts struck down the death penalty laws in the early 1980s and the last executions in the state were in the late 1940s. But Tsarnaev and Sampson were charged with federal crimes that allow capital punishment; in Sampson’s case, it was the crimes of carjacking resulting in death.

Scott McCloskey, one of Philip McCloskey’s six children, said after the verdict was announced that he was disappointed that jurors did not choose the death penalty for his father’s killing, but he took solace in the verdict.

“When all is said and done, he got the death penalty, and that’s what we set out for,’’ he said. “We got the result we wanted.’’

Mike Rizzo, Rizzo’s father, called the verdict a team effort, saying the families of Sampson’s three victims have been unified since Sampson changed their lives more than 15 years ago.

“This is a good day for the Whitney, the McCloskey, and the Rizzo families,’’ he said. “It’s a very sobering and somber day for us, but we know justice has prevailed.’’

Sampson will now engage in a lengthy appeals process. Since modern federal death penalty laws went into effect in the late 1980s, only three of more than 500 federal defendants who faced capital punishment have been executed; the remainder had their cases overturned, are appealing their death sentence, pleaded guilty to lesser charges, or had charges dismissed.

Sampson pleaded guilty to killing Rizzo and McCloskey, but his lawyers sought a sentence of life without the possibility of parole.

Sampson had also pleaded guilty to killing his third victim, Robert “Eli’’ Whitney, in New Hampshire and received a life sentence in that state. But jurors in Sampson’s federal trial in Massachusetts were allowed to consider Whitney’s murder when deciding a sentence.

Throughout his trial, jurors heard gruesome details of the killings, including Sampson’s taped confessions. He admitted carjacking McCloskey, who was driving to Weymouth to meet a friend who would help with his taxes, and directing him into the woods at knifepoint. He dragged him up a hill and stabbed him multiple times.

After wandering through communities in the South Shore, he got in a car with Rizzo, directed him at knifepoint to woods in Abington — not far from where Sampson grew up — tied him to a tree with yellow rope and stabbed him repeatedly.

He then drove Rizzo’s Volkswagen Jetta to New Hampshire where, after a day of wandering, he broke into a home.

He killed Whitney, a maintenance man who was tending to the home. He told authorities that, tired of the blood from the stabbings, he strangled Whitney for several minutes and left him in the bathroom while he explored the home. He drank beer and made breakfast.

Sampson then tried to carjack a fourth person, who escaped. He broke into another home and called authorities to turn himself in.

Throughout the trial, Sampson’s lawyers portrayed him as a mentally ill man who had a troubled upbringing and suffered years of physical and emotional abuse. He experienced repeated trauma during previous stints in jail, and they say he had an emotional breakdown leading up the killings. Before the murders, he tried to turn himself in to the FBI.

In a lengthy verdict slip, at least some of the jurors accepted the mitigating factors Sampson’s lawyers listed in their attempt to explain some of his actions: that he had a learning disability; that his father abused him; that he suffered from drug and alcohol addiction and mental illness.

But jurors unanimously rejected the notion that Sampson had remorse for his crimes, however, an indication that his late-trial apology to the families, in the form of a statement in front of jurors, did not aid in his defense.

When asked whether Sampson took responsibility for the killings, jurors said no.

Jurors could not be reached to explain the split verdict in choosing the death penalty for the killing of Rizzo but not McCloskey. But they may have paid attention to Sampson’s own statement that, while the killing of McCloskey was the result of an emotional outburst, he had planned out Rizzo’s killing.

“It was premeditated,’’ he said in his confession.

Milton J. Valencia can be reached at milton.valencia-@globe.com. Follow him on Twitter @miltonvalencia.