BOGOTA, Colombia - Colombia's main rebel group killed four of its longest-held captives, whose bodies were found Saturday after soldiers fought with guerrillas, the government said.

"They were held hostage for between 12 and 13 years and wound up cruelly murdered," President Juan Manuel Santos said of the three police officers and a soldier.

He called the killings "a crime against humanity" and dismissed any suggestions that Colombia's armed forces might be responsible.

Defense Minister Juan Carlos Pinzon said government troops, who had been in the area for 45 days chasing rebels, had intelligence that the guerrillas might be holding police and soldiers as captives.

No official explained the nature and reliability of that intelligence or whether the four died in a failed rescue mission.

All four men were killed execution-style, three with shots to the head and one with two shots to the back, Santos told a community meeting in central Colombia.

Neither the president nor Pinzon, who was first to announce the deaths and did not take questions from reporters, said whether the four were believed to have been killed Saturday. Pinzon said the bodies were found together, with chains near them.

It is standing policy of the leftist Revolutionary Armed Forces of Colombia, or FARC, to kill captives to prevent their rescue. And the rebels frequently chain their captives.

The sister of one of the victims, 34-year-old police Maj. Elkin Hernandez, was angry with the government.

"The FARC are murderers for the manner in which they killed them, and the government is equally a murderer. They had the possibility to get them out of there, and they didn't," Margarita Hernandez told The Associated Press.

Former Sen. Luis Eladio Perez, who was freed by the FARC in February 2008 after six years of captivity, told the AP he believed the four died in a failed rescue.

The bodies were found about 10 a.m. in the southern state of Caqueta. Among them was the longest-held rebel captive, Sgt. Maj. Jose Libio Martinez. He was seized by rebels Dec. 21, 1997, in an attack on a lonely southern mountain outpost called Patascoy.

Their killings left the FARC in possession of about 16 security force members, which they consider to give them political leverage.

The FARC took up arms in 1964 and are Latin America's last remaining rebel army. They have suffered a series of military setbacks and record desertions in recent years, crowned by the Nov. 4 combat death of their leader, Alfonso Cano.

His successor, Timoleon Jimenez, was named the following day and few analysts believe defeat is imminent for the rebels, who draw their strength from landless peasants in a country where land ownership is concentrated in a few hands. The FARC are believed to comprise about 9,000 fighters.

The drug trafficking-funded rebels have periodically freed security force members and politicians as goodwill gestures, stepping up releases in early 2007 with the intercession of Venezuelan President Hugo Chavez.

But Santos, who was defense minister for four years before winning the presidency, has publicly refused to entertain peace overtures, saying the rebels must first show themselves willing by freeing all captives.

Analyst Ariel Avila of the Nuevo Arco Iris think tank said Saturday that the killings will give the government justification not to negotiate. "But the government won't get out of this without blame," he added.

On several occasions, the FARC has slain hostages when under military pressure, real or perceived.

In June 2007, FARC fighters killed 11 regional lawmakers they had kidnapped five years earlier, apparently under the mistaken belief they were under attack by government forces.

In 2003, rebels killed 10 captives, including a former defense minister and governor, during an attempted rescue when they heard approaching military helicopters.

The FARC suffered a major embarrassment in July 2008 when elite Colombian troops posing as international humanitarian workers rescued former presidential candidate Ingrid Betancourt, three U.S. military contractors and 11 others in a daring ruse.

Reached by the AP via email about the deaths of four men with whom she had for a time shared captivity, Betancourt said: "The truth is that the news has hit me hard. I'm in pain and don't wish to make any (further) comment."

Betancourt last year published "Even Silence Has an End," an eloquent recounting of her more than six years in captivity.