A federal jury could decide as early as this week whether to execute a Brooklyn murderer or spare his life.

The convict, Martin Aguilar, is the first of two men who will be sentenced for capital murder this month in U.S. District Court in Brooklyn. The two cases end a three-year period without any death penalty proceedings in this federal courthouse at Cadman Plaza.

No federal jury in New York has voted for death in the last 53 years. Still, death penalty attorneys are following the Brooklyn federal courthouse closely, as there is an unusually high number of capital cases. A second jury will reconvene next week to decide whether to impose a sentence of death in an unrelated case. In that case, the defendant, Ronell Wilson, was convicted last month of murdering two police officers in 2003.

The jury that reconvened yesterday for the death penalty phase of Aguilar’s trial is the same panel that convicted him last month for his role as the triggerman in a 2000 murder-for-hire case. Aguilar committed the murder to settle a drug debt and buried the body of the victim, Jose Fernandez, at the bottom of a storm drain in a Brooklyn cemetery, prosecutors said.

In addition to the gruesomeness of the crime and the lack of remorse Aguilar showed in the aftermath, prosecutors said yesterday that a death sentence was warranted because Aguilar, 33, was a menace to others, even when behind bars.

An assistant U.S. attorney, David Bitkower, said Aguilar “will be dangerous to the people around him, when much less is at stake” in the event that the jury voted to impose a life sentence.

In the month leading up to his trial last year, Aguilar stabbed another inmate, Mr. Bitkower said. That stabbing occurred in the law library of the federal jail in Brooklyn while the victim was handcuffed.

Federal prosecutors depicted the sum of Aguilar’s life to be a series of violent acts perpetrated across the entire length of the city, from the Verrazano Bridge northwards to the Bronx.

Some of these assaults and killings are documented in court proceedings, others not. A government witness, Jeffrey Taylor, who was an accomplice in the murder-for-hire case, told the jury how Aguilar used to boast to him about his crimes.

For instance. Mr. Taylor said, that in the 1990s Aguilar told him he shot at couples in parked cars near the Verrazano Bridge “for the fun of it.”

Mr. Taylor also testified that Aguilar, a member of the Latin Kings street gang, had spoken of shooting two drug dealers in the Bronx. Mr. Taylor was prevented from saying more, when the judge, Raymond Dearie, instructed the jury to disregard that evidence.

Prosecutors focused much of their efforts yesterday in telling the jury about a 1991 killing attributed to Aguilar. In a fight that occurred in a schoolyard in Sunset Park, Aguilar killed a man, Antonio Rodriguez Marrero, by stabbing him in the back and right temple with a screwdriver, according to two eyewitnesses. Although Aguilar was acquitted of murder for that fight, it could prove significant as this jury weighs Aguilar’s life.

A lawyer for Aguilar called on the jury yesterday to “reject another death by the federal government.”

The lawyer, Louis Freeman, listed several reasons why Aguilar’s life should be spared. Mr. Freeman questioned whether the murder-for-hire deserved a sentence of death.

“We also suggest this murder was not especially cruel or heinous,” Mr. Freeman said.

Mr. Freeman called Aguilar a “complicated human being whose life is worth saving.” He encouraged the jury to consider Aguilar’s childhood circumstances including the cruelness that Aguilar’s father exhibited.

Expanding on that theme, Mr. Freeman said Aguilar’s “first significant memory” involved his pet rabbit being slaughtered by his father.

The father wanted to “teach him a lesson,” Mr. Freeman said.

In what is expected to be a major theme in Aguilar’s defense, Mr. Freeman appealed to the jury’s sympathy for Aguilar’s mother, Elizabeth, who has attended each day of her son’s trial.

“We’re going to demonstrate the effect an execution would have on her and on his brothers,” Mr. Freeman said.

Wearing a white turtleneck, Aguilar followed the proceedings energetically, but appeared distracted at times and turned in his chair continuously. After the jury had left at the end of yesterday’s proceeding, Aguilar blew his mother, Elizabeth, a kiss and mouthed “I love you” to where she sat in the front row.