The "video for peace," released by the Revolutionary Armed Forces of Colombia, or FARC, came a week after Colombian President Juan Manuel Santos said on TV his government had held "exploratory conversations" with the Marxist-Leninist group to end the 48-year armed conflict.
Santos said Colombia's second-largest rebel group, the National Liberation Army, or ELN, indicated a readiness to talk.
ELN did not immediately confirm its involvement in the talks.
Both groups, which finance their operations through narcotics trafficking and kidnapping for ransom, are labeled terrorist organizations by Colombia, the United States and the European Union.
"We are coming to the negotiating table without rancor or arrogance," FARC top commander Rodrigo Londono, known by his war alias Timochenko, said at the beginning of the video, first posted on the FARC Web site and later found on YouTube, before the singers began rapping.
President Barack Obama said the United States welcomed the development.
In a statement issued by the White House, the president said the "Santos administration has demonstrated an unwavering commitment to seeking a durable peace and ensuring a better life for all Colombians through its security and social inclusion policies."
The talks are to begin in Oslo, Norway, in early October, and then move to Havana, Bogota's El Nuevo Siglo newspaper reported, adding details were expected to be made public this week.
In the video, a young man and a woman wearing T-shirts emblazoned with 1960s Argentine Marxist revolutionary Che Guevara's name and FARC emblems rap about traveling to Cuba to negotiate with the Colombian government. They brag the government wasn't able to defeat them.
Others dressed in olive-green uniforms play drums and a guitar in a rural background.
"I'm going to Havana, this time to talk to the one who accused me of lying about peace," the singers rap. "The bourgeois who was looking for us couldn't defeat us."
The lyrics, which say Venezuela was instrumental in the negotiations, cynically add they expect negotiators will try to "cajole" FARC.
After the song, Londono returns to the video and says, "We have sworn to win and we will win."
A government spokeswoman told The Wall Street Journal it would not comment on the video.
Santos -- who is mocked in the video as "that pedantic Chucky Santos who finds the need to ask [former Cuban leader] Fidel Castro to help with FARC" -- responded to Londono's statement "with much hope" that both sides "can settle this conflict, which has caused so much pain."
"Chucky" referred to the homicidal Chucky doll in the 1990s horror film series "Child's Play."
Colombia has said military operations against the rebels will continue even as the talks proceed, with Santos warning Monday against "repeating the mistakes of the past," when Colombia gave FARC a large safe haven as a confidence-building measure in the last talks a decade ago -- but FARC used the territory to train troops and continue its drug trafficking. Those talks ended in failure.
Once numbering about 18,000 fighters, FARC currently has an estimated 8,000 combatants.