He said another rebel-held Colombian soldier, Lieutenant Colonel William Donato, fled for his life during the confrontation with rebels and that his fate was still unknown.
"We have high hopes that he is in hiding and that he will be found in the coming hours," Silva said on Sunday.
Alvaro Uribe, the Colombian president, has been pushing Farc rebels into remote jungles and mountains in a concerted US-backed security drive.
"They are fighting in the jungles of Guaviare to get them out," Uribe said. "They are both in the hands of our armed forces."
Farc rebels are still holding about 20 military and police officers in captivity.
Sunday's rescue is the highest profile operation since a 2008 mission that freed Ingrid Betancourt, a former Colombian presidential candidate, and three US contractors who were kidnapped when their airplane crashed while on an anti-drug mission.
Both Mendieta and Murillo were captured by the Farc when rebels overran Mitu town in the jungle province of Vaupes in November 1998, and have since been seen only occasionally in hostage videos.
"I can't believe it, I am the happiest woman in the world, I am dying to hug him after so many years of absence," said Maria Teresa de Mendieta, the rescued general's wife.