San Juan, Puerto Rico (Reuters) - A federal jury is deciding whether to give an island man the death penalty in a potentially landmark case highlighting Puerto Rico's relationship with the United States.

The jury entered its third day of deliberations on Thursday. Last month, it convicted Edison Burgos Montes, a Yauco merchant, of the 2005 killing of his girlfriend, Madelyn Semidey Morales, who was a Drug Enforcement Administration informant set to testify against him for drug trafficking offenses.

The Puerto Rico constitution forbids capital punishment, but U.S. prosecutors can seek execution and say they are often required to do so in specific types of murders, such as the killing of a federal officer, or in this case, a federally protected witness.

More than 60 federal crimes qualify for the capital punishment, but Washington prosecutors ultimately decide whether to go forward on a case-by-case basis.

While the U.S. government also seeks capital punishment in 17 other states that also do not carry out executions, many Puerto Rico critics see its attempt to bring capital punishment cases against island criminals as an unwelcome federal imposition on local affairs.

The jury is deliberating as the island prepares for a November plebiscite in which Puerto Ricans will decide whether they want to change from the current "commonwealth" status as a U.S. territory.

Opposition to the death penalty cuts across political lines, however.

As the jury started deliberations earlier this week, Governor Luis Fortuno and Resident Commissioner Pedro Pierluisi, Puerto Rico's sole representative to the U.S. Congress, spoke out against the death penalty. Both members of the pro-statehood New Progressive Party are up for reelection the day of the plebiscite.

Meanwhile, Senator Alejandro Garcia Padilla, the pro-commonwealth Popular Democratic Party candidate for governor, said he would work to end federal capital punishment prosecutions involving Puerto Rico residents.

This is the fourth death penalty conviction sought by U.S. authorities since capital punishment was eliminated on the island in 1929, two years after the last execution.

Juries opted for life over death in 2006 for a man who killed a Veteran's Administration security guard and in 2002 for two men accused of killing a security guard during an armored car robbery. In the final case, a jury acquitted two men of killing a grocery store owner during a 2003 trial in which federal prosecutors sought the death penalty.

However, many people believe that local juries will eventually approve a death penalty verdict because of the island's high rate of violent crime, which peaked last year at more than 1,100 homicides, a record.

"If it's not this case, it will be the next one or the one after that, but it's coming down the road," radio commentator Enrique Cruz told listeners after the jury ended its second day of deliberations. "There will be a jury that wants to send a message."

Two more death penalty cases are due to be heard next year, according to U.S. law enforcement officials.

Under an agreement with the Fortuno administration, federal authorities have assumed jurisdiction in carjackings, public shootings and other lesser crimes.

As a result, federal prosecutions on the island have nearly doubled over the past year to 4,226.

(Edited by David Adams and Lisa Von Ahn)