* Troops to continue operations against rebels
* Talks could take place in Cuba or Norway - source
* Santos pledges to learn from failed peace process
By Helen Murphy and Luis Jaime Acosta
BOGOTA, Aug 27 (Reuters) - Colombia's government is seeking peace with the country's biggest rebel group, the FARC, and could consider also holding talks with a second guerrilla movement to end five decades of war, President Juan Manuel Santos said on Monday.
In a televised address from the presidential palace, Santos said his government would learn from the mistakes of so many previous leaders who tried but failed to clinch a lasting ceasefire with the Revolutionary Armed Forces of Colombia.
"Since the first day of my government I have completed my constitutional obligation to find peace. With that aim, we have had exploratory conversations with the FARC to seek an end to the conflict," he said, confirming weeks of swirling rumors that his government had started behind-the-scenes discussions.
He added that the military would continue its operations "throughout every centimeter" of Colombia while talks continued.
Santos did not provide further details, but said he would reveal more about the talks in the coming days.
A successful peace agreement with the rebels would secure him a place in history as the leader who ended a conflict that has killed tens of thousands over the years and left the Andean nation's reputation in tatters.
In response to a Reuters interview published on Monday with the head of the nation's second biggest rebel group, Santos said the National Liberation Army, known as the ELN, could also be involved in the peace talks.
"Today the ELN has expressed, via an international news agency, its interest in participating in conversations to put an end to the violence," the president said in his brief speech.
"I tell that group that, within the same framework, they too can be part of the effort to end the conflict."
A Colombian intelligence source told Reuters earlier that as part of the deal to hold talks, Santos had agreed FARC rebels would not be extradited to any other country to stand trial.
Details are still being worked out, the source said, but the negotiations could take place in Cuba or Norway. U.S. President Barack Obama is aware of the process and is in agreement, the source said.
Santos, who is at the mid-point of his four-year term, has said he would consider peace talks with the FARC only if he was certain the drug-funded group would negotiate in good faith.
The last peace effort ended in shambles.
In 1988 former President Andres Pastrana ceded the FARC a safe haven the size of Switzerland to promote talks. The rebels took advantage of the breathing space to train fighters, build more than 25 airstrips to fly drug shipments, and set up prison camps to hold its hostages.
News of the latest peace effort was met with guarded hope among Colombians.
"Honestly, full peace is probably never possible. Of course it would be good ... but really, an end to the war? I think an end to the world will happen first," said Maria Eugenia Martinez as she sold cigarettes in an upscale Bogota neighborhood.
Santos discussed the peace process during talks in Havana with Venezuelan President Hugo Chavez and Cuba's former leader Fidel Castro before the Summit of the Americas in Cartagena, Colombia earlier this year, the intelligence source said.
Colombia's congress passed a constitutional reform in June that set the legal basis for eventual peace with the rebels. The reform prohibits guerrilla leaders accused of crimes against humanity from holding political office.
In a recent interview with Reuters, Santos said he would only start a peace process "with a high probability of success. I would not start a process to fail."
News of the talks had already angered Santos' predecessor, Alvaro Uribe, who has slammed Santos for wanting "peace at any cost" and allowing the rebels to rearm and regroup.
Santos, a former defense minister, won election in 2010 by a landslide, pledging to cut unemployment and continue Uribe's hard line security policies, while fostering economic growth and reducing poverty.
While much of the world struggles to shore up fiscal accounts, Colombia's financial management, buoyant economy and security advances have helped shield its economy from too much fallout from the international financial crisis.
Once an outcast for most foreign companies, the Andean nation has become a magnet for investment as a U.S.-backed offensive against the FARC sharply reduced the number of kidnappings and murders. The nation was rewarded last year with an investment grade from three major credit-rating agencies.
But the 61-year-old Santos has seen his own ratings slide in recent weeks amid criticism that he had allowed rebels to chip away at the security gains of the last decade.
Attacks on oil industry installations have jumped 40 percent over the last year, while violent clashes between troops and indigenous protesters led to withering criticism of Santos for not protecting the soldiers.
Six people were killed, including two children, in a FARC bomb attack in central Meta province on Sunday.
The FARC, which calls itself "the people's army" defending peasant rights, has battled about a dozen governments since appearing in 1964, when its founder, Manuel Marulanda, and 48 rebels fought off thousands of troops in jungle hide-outs.
The group has faced its biggest set-backs in recent years as U.S.-trained special forces use sophisticated technology and spy networks to track the leaders.
A string of defeats began in 2008 with a cross-border military raid into Ecuador that killed its second in command. Marulanda died of a heart attack weeks later and was replaced by Alfonso Cano, who was later killed too.