The president's older brother, journalist Enrique Santos, said in response to emailed questions that he didn't believe the government had given the FARC an ultimatum.
"The process is going through a difficult moment but I don't see a breakdown in the short term," said the former co-director of the El Tiempo newspaper, who took part in the secretive first round of talks but is not the current negotiations. "My concern is the very slow pace of the agenda."
The FARC has stepped up hit-and-run attacks since Jan. 20, killing three customs police officers in a highway ambush in the northeastern state of Guajira Friday. The same day, it launched a three-week "armed strike" in the poor, mostly rural northwestern state of Choco, vowing to halt and torch any vehicles that take to the highway in the state.
Authorities reported nearly full compliance to the strike Friday, and a police colonel told The Associated Press on Saturday that authorities had not yet restored order. The colonel spoke on condition of anonymity because he was not authorized to speak with the media.
Colombia's military said it had killed six rebels, including a front commander, in a bombing raid early Thursday in Tierralta, a traditional FARC stronghold in the northwestern state of Cordoba.
The talks in Havana are tackling the first and perhaps most difficult issue on a five-point agenda: agrarian reform.
Presidential elections are scheduled for May 2014, and President Santos says he will announce after June whether he intends to run for re-election.
Associated Press writers Vivian Sequera in Bogota and Frank Bajak in Lima, Peru contributed to this report