In a videotaped plea aired on national television, Betancourt said she favours military intervention to free her, but that it would have to be "a decision of conscience by President Alvaro Uribe."
"A rescue, yes, absolutely ... but not any kind of rescue. Rescues are either successful or they shouldn't happen," said Betancourt, looking thin but healthy.
Uribe has taken a cautious approach saying, “the government must deal with this issue very prudently. The Defence Ministry has to analyse it.”
The Revolutionary Armed Forces of Colombia, known by its Spanish initials FARC, kidnapped Betancourt at a roadblock in February 2002 with hopes of exchanging her for jailed comrades.
"It is very important that it is the president who evaluates the risk, and for that matter the chances of success... I trust him."
Military rescues are risky operations in Colombia. The heavily armed FARC executed a former defence minister, governor of Uribe's home province, and eight military personnel in May instead of turning the hostages over to an advancing military rescue team.
Betancourt said she heard of those deaths, but authorised a rescue attempt anyway.
"It is very important that it is the president who evaluates the risk, and for that matter the chances of success ... I trust him," she added, a rosary wrapped around her hand.
Uribe, whose father was killed by rebels during a kidnap attempt, took office a year ago promising to get tough with Latin America's largest and oldest guerrilla army. The four-decade-old war claims thousands of lives a year.
His defence minister, Marta Lucia Ramirez, said the armed forces had a responsibility to find and free Betancourt, a dual French-Colombian national.
The French-schooled politician was one of nearly 3000 people abducted last year in Colombia. Most victims are sold-off by rebels for ransom money.
Meanwhile Colombia's high commissioner for peace said on Sunday that United Nations delegates and leaders of the FARC were examining whether to meet for talks in Brazil.
UN special advisor on Colombia James LeMoyne and FARC spokesman Raul Reyes are in contact and will shortly hold a meeting to discuss Colombia's armed conflict, the commissioner.