President Alvaro Uribe made the decision after a car bombing at the military university on Thursday injured 23 people. The government has blamed the attack on the Revolutionary Armed Force of Colombia (FARC) but it has denied any involvement.
"The only path that remains is a military rescue," Uribe said on Friday, adding that the government had intercepted phone calls from a rebel leader which proved that FARC had planted the bomb.
"We cannot continue the farce of a humanitarian exchange [of prisoners] with the FARC."
FARC issued a statement on its website suggesting that the bomb was planted by the US in an attempt to destroy the possibility of ending Colombia's four-decade-old guerrilla war.
Sixty-two hostages - including three American defence contractors and former Colombian presidential candidate Ingrid Betancourt - were to be swapped for guerrillas being held in government jails.
Families of the hostages have condemned Uribe's decision as dangerous.
Families of kidnap victims have
criticised Uribe's decision
French-Colombian citizen Ingrid Betancourt was kidnapped while campaigning in 2002 and the Americans, Marc Gonsalves, Thomas Howes and Keith Stansell, were taken while trying to locate crops used to make cocaine in 2003.
Mariana Howes, Thomas Howes' wife, called the idea of a military rescue "crazy".
"He's going to get my husband killed," she told Reuters news agency.
The group executed a group of hostages, including a former defence minister, during a failed military rescue in 2003.
The decision came less than a month after Uribe said he was willing to discuss a FARC proposal to withdraw government troops from a rural area almost the size of New York City to negotiate the exchange.
The president has started peace talks with a smaller rebel group, the National Liberation Army, or ELN, and disbanded right-wing paramilitaries but peace with the 17,000-strong FARC remains elusive.
FARC still control large rural areas of Colombia, funding their operations through the country's multibillion-dollar cocaine industry.