By Sam Karlin

BATON ROUGE, La. (Reuters) - U.S. Vice President Joe Biden and Attorney General Loretta Lynch called for unity to honor three slain Louisiana police officers, speaking at a memorial service on Thursday in Baton Rouge where they were gunned down this month by a U.S. Marine Corps veteran.

Several hundred people and dozens of law enforcement officers attended the vigil, where Louisiana Governor John Bel Edwards also implored the community to seek peace and healing after the July 17 attack that also wounded three other officers.

The shootings came amid a series of deadly encounters igniting debate over policing and minorities in the United States. The killings rattled a city already grappling with protests after the fatal police shooting on July 5 of Alton Sterling, a 37-year-old black man confronted by officers while selling CDs outside a convenience store.

Biden said he heard that Sterling's aunt, who raised him, had prayed with a slain officer's father.

"Loss is loss is loss," he said, speaking at a church in Baton Rouge, the state capital. "Now the city has to reach out, the country has to reach out to law enforcement, and let you know how much we care."

On the stage behind him, three chairs sat empty, decorated with sashes and uniform caps representing the officers.

Choking back tears, two of the officers' wives recalled phone calls and door knocks on an initially normal Sunday morning that changed their lives forever.

Slain Baton Rouge police officers Matthew Gerald, 41, and Montrell Jackson, 32, and East Baton Rouge Sheriff's Deputy Brad Garafola, 45, were killed in what Louisiana officials described as a calculated attack. Shooter Gavin Long, 29, a black former Marine with ties to an African-American anti-government group, was also killed in an exchange of gunfire.

"No family should ever have to be without their loved ones, especially when these three heroes could be home had a person not been filled with so much hatred," said Tonja Garafola.

Jackson's wife, Trenisha, recalled his wish to see healing in the city and directed the crowd to repeat sentiments that he had posted on Facebook in the tense days before his death.

"I will not let hate infect my heart," the crowd repeated.

The assault followed the deaths of five officers in Dallas, Texas on July 7, who were shot by another black former U.S. serviceman. President Barack Obama traveled to Dallas in the wake of those shootings.

One of the wounded Louisiana officers, Nicholas Tullier, 41, remains hospitalized in critical condition, the East Baton Rouge Sheriff's Office said on Thursday. At the vigil, Sheriff Sid Gautreaux said he is "fighting for his life."

(Writing by Letitia Stein; Editing by Colleen Jenkins and James Dalgleish)