He has told government negotiators to travel to to Cuba to consult Farc leaders on the next move.
President Santos has promised to "continue the search for peace until the last moment of my mandate because that's the way to leave a better country to our children".
"I won't give up," he said.
The Farc leader known as Timochenko also said that the rebels remained committed to securing an end to the conflict.
"The Farc reiterates its disposition to use only words as a weapon to build toward the future," he said after the result.
"Count on us, peace will triumph."
But before the vote, President Santos had told the BBC that there was "no Plan B" for ending the conflict, which has killed an estimated 260,000 people.
He said he would meet all political parties on Monday to discuss the next steps and "open space for dialogue".