The Colombian government and the National Liberation Army (ELN), an anti-government group, began their sixth round of peace talks on Tuesday.
Both sides told reporters in the Cuban capital about the substantial difficulties in the talks, which began in December 2005.
This round of talks came five days later than the original schedule as the ELN team had problems getting to Cuba until the Colombian government arranged a charter flight.
ELN chief negotiator Pablo Beltran and the government's peace envoy Luis Carlos Restrepo are expected to hold talks for at least six days on this occasion.
In Bogota, the Colombian government on Tuesday issued a statement, calling for the ELN to fulfill what it promised during talks in December 2005 and hoping for a breakthrough in the upcoming talks.
On Monday, Beltran told the media that the ELN was ready to end hostilities toward the government immediately as an "experiment to create an environment of peace."
Beltran also confirmed for the first time previous reports that Colombian Nobel Prize-winning novelist Gabriel Garcia Marquez and Cuba's acting president Raul Castro met with ELN leaders and Restrepo in mid-March in efforts to push the ELN-government peace negotiations forward.
The ELN was willing to sit down for a discussion with the government on how to realize a ceasefire, Beltran said. But he turned down the government suggestions to bring all ELN soldiers together in one place, calling it a suicidal move.
The ELN, Colombia's second-largest anti-government organization after the Revolutionary Armed Forces of Colombia, has been fighting the government since the 1960s. But its forces have dwindled to fewer than 2,000 fighters from some 4,500 after a series of military offensives by government forces in recent years.
The country has been locked in a four-decade civil war, the longest in Latin America, in which government forces, guerrillas and paramilitaries are fighting one another. The conflicts kill more than 3,000 people every year.