* Santos calls for confidentiality to be maintained
* President has rejected changes to political, economic model
* FARC ceasefire ends on Sunday; concern over renewed attacks
By Helen Murphy
BOGOTA, Jan 16 (Reuters) - Colombia's President Juan Manuel Santos on Wednesday opened the door to a popular vote on any peace accord negotiated and signed with FARC rebels but rejected a guerrilla demand to change the constitution if a deal is clinched.
Talks to bring an end to Latin America's longest-running insurgency began in Cuba in November, when the government and the Revolutionary Armed Forces of Colombia, known as the FARC, sat down for the first round of a five-point peace agenda.
Ivan Marquez, head of the FARC negotiating team, has called for a national assembly to alter Colombia's charter and ensure any agreements would be set in stone.
The FARC, which has fought successive governments since 1964, reiterated their demand on Tuesday. But Santos rejected the idea.
"It's very possible that we could find a way to seek popular approval for any accord," Santos said in an address in the Norte de Santander province. "That's still to be discussed."
"But I want it to be very clear that we will not end these agreements with a national assembly."
Santos has repeatedly ruled out discussing major changes to Colombia's economic or political model, saying that if the guerrillas want to modify the system, they should join the political process and win elections.
More than 20 years ago, Colombia held a nationwide assembly to rewrite the 1886 constitution. Demobilized rebels from smaller groups participated but not the FARC or the National Liberation Army, another left-wing group.
Harvard-educated Santos urged the FARC on Wednesday to keep discussions between negotiators strictly confidential until the accords are reached.
"The dialogue has to be serious, it has to be a discreet dialogue," said Santos, 61. "Only when there are agreements, important advances ... only when those advances exist will we inform the public, the national and international community."
The FARC was angered by a recent newspaper column written by Santos' brother, who detailed the background of his involvement in the secret negotiations to bring the two sides to the table. The FARC threatened to ditch a confidentiality agreement during the negotiations.
Santos, first as defense minister under former President Alvaro Uribe and later as Colombia's leader, has dealt the group some of its biggest blows, killing senior leaders and hitting units responsible for financing operations.
The FARC has said it will lift its two-month-long unilateral ceasefire on Sunday, raising concern a re-energized group will launch new attacks against military and civilian targets.
Negotiations were formally launched on Oct. 18, but the talks immediately got off to a rocky start after the guerrillas said they wanted to discuss a range of topics not specifically mentioned in the agenda.