Mr Cuellar's death provoked widespread shock and revulsion
Left-wing rebels in Colombia have said they killed a provincial governor shortly after seizing him from his home at gunpoint on 21 December.
A Farc rebel statement said the aim had been to try Luis Francisco Cuellar for corruption and paramilitary ties.
His "tragic" death had resulted from a government order to use force to rescue rebel-held hostages, the rebels said.
Government officials and Mr Cuellar's family said the rebels were trying to justify the unjustifiable.
Mr Cuellar, the governor of the southern province of Caqueta, was found dead less than a day after he was seized.
He was the highest profile politician to be kidnapped since 2002.
The authorities immediately blamed the Revolutionary Armed Forces of Colombia (Farc) for his murder, and said he had probably been killed as troops closed in on his kidnappers.
The Farc statement appeared on Tuesday on the Anncol news agency website, which regularly carries rebel communications.
"Despite the obvious links between... Luis Francisco Cuellar and paramilitaries, the aim of holding him was not to kill him nor demand a ransom but to put him on trial for corruption," the statement, dated 24 December, said.
Mr Cuellar's death had been a direct consequence of President Alvaro Uribe's order to use force to rescue hostages being held by the guerrillas, the Farc said.
But Colombia's peace commissioner, Frank Pearl, told El Tiempo newspaper: "They are trying to justify with absurd words an absurd and unjustifiable crime."
The guerrillas were thought to number some 16,000 fighters, but analysts suggest their ranks have fallen to about 9,000.
They suffered a series of defeats at the hands of the security forces in 2008, but they are still holding more than 20 police officers and soldiers, often referred to as "high-profile" hostages, seized more than a decade ago.
They are also believed to have kidnapped hundreds of other people, mainly for ransom.