Colombian President Juan Manuel Santos and opposition rival Alvaro Uribe have met in a bid to resolve differences over a peace deal with Marxist FARC rebels that was rejected in a shock vote this week.
The two expressed a willingness to seek an end to the 52-year war that has killed more than 220,000 people and displaced millions more.
The president voiced optimism afterwards that Colombia can end a half-century war with the FARC rebels, saying: "Peace in Colombia is close and we will achieve it."
Sunday's surprise referendum result, which confounded pollsters and was a political disaster for Mr Santos, plunged the country into uncertainty over the future of the Revolutionary Armed Forces of Colombia (FARC) rebels.
FARC rebels had been expected to disarm once the deal was passed by voters.
After more than three hours of talks, former president Uribe emphasised the need for "adjustments and proposals that should be introduced ... to seek a new peace deal that will include all Colombians".
Without giving any concrete proposals, Mr Uribe said Mr Santos had shown he was disposed to changes.
Mr Uribe opposed Mr Santos' peace talks from the start and said the final deal, which was reached in August after four years of painstaking negotiations in Havana, gave too many concessions to the rebels.
He spearheaded the No campaign, urging Colombians not to approve the accord, which would have given the FARC guaranteed congressional seats and immunity from traditional jail sentences.
The No side carried the day by less than half a percentage point.
"We identified that many of their worries come from points that need clarification or precisions. Today we began to work with them to firm up those points and resolve their doubts," Mr Santos said in a statement.
The future of the deal seems to hang on whether the FARC will accept tougher conditions for demobilisation, perhaps combined with a softening of Mr Uribe's hardline demands.
Mr Santos once served in Mr Uribe's cabinet, but the two have not met since late 2010.
The government has said the decision to reopen talks lies with rebel leadership.
Government negotiators are in Havana to confer with guerrilla commanders who have said they will remain "faithful" to the accord.
A senior US State Department official said today the government and rebels are committed to dialogue to reach agreement.
"They have made it clear they want the peace process to continue and they want to negotiate a settlement," the official told reporters on a conference call.
He said he had met both sides in Havana, Cuba.