The Farc leader, known as Timochenko, said he was prepared to review and "fix" the agreement, after many in the "no" camp said it was too lenient.
Talks between rebel leaders and government negotiators were due to take place in Cuba on Monday.
The deal was signed last week after nearly four years of negotiations.
It is not yet clear what can be done to save the deal. President Santos earlier said there was no "Plan B" for ending the conflict, which has killed about 260,000 people.
"I will not give up, I will keep seeking peace until the last minute of my term," he said in address after the results were announced.
The chief peace negotiator for the government, Humberto de la Calle, offered to resign on Monday, saying he took "full responsibility for any errors in the negotiation". He was earlier ordered back to the Cuban capital of Havana to work with rebel leaders on modifying the deal.
Former President Alvaro Uribe, who led the "no" campaign, is demanding prison sentences for rebel leaders found guilty of crimes and wants them banned from politics.
Colombia referendum: Peace talks to be revived despite `no` vote
04 October 2016
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Colombian President Juan Manuel Santos has vowed to continue working for peace despite the shock rejection of a deal with Farc rebels by 50.2% of voters.
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