(Adds leftist Clara Lopez saying she will not back any candidate in run-off)
By Julia Symmes Cobb and Peter Murphy
BOGOTA, May 29 (Reuters) - Colombian presidential candidate Oscar Ivan Zuluaga, who faces incumbent Juan Manuel Santos in a run-off vote, on Thursday dropped his threat to end peace talks with Marxist rebels if elected, softening his stance on the election's most pivotal issue.
The right-wing Zuluaga won the most votes in a first round vote on Sunday but not enough to avoid a run-off set for June 15. He is now neck and neck with Santos, a poll showed on Thursday, raising the suspense in the Andean nation's tightest election in years.
Zuluaga told Caracol radio that if elected, he would still demand that the Revolutionary Armed Forces of Colombia, or FARC, cease combat and criminal activity to continue the talks Santos initiated in late 2012, but would no longer immediately suspend talks as he promised previously.
Zuluaga did not say how long he would give FARC to declare a ceasefire, a condition it has rejected until now, but said he softened his stance at the request of Conservative Party leader Marta Lucia Ramirez in exchange for her support in the run-off vote campaign.
"We maintain our same conditions to advance the search for a negotiated peace," Zuluaga told local radio. "We'll allow the talks to continue." He added he would review what had been agreed upon so far during the closed-door discussions.
The question of how to end the country's 50-year conflict, during which 220,000 people have been killed, has been the campaign's most prominent issue, with negotiations appearing to put peace within closer reach than ever before.
Negotiators at the talks, which are being held in Cuba, have reached partial accords on three of five topics under discussion.
Santos says this election is a choice between grasping a historic chance to end the decades-old conflict by voting for him, or continuing "an endless war" by choosing his rival.
Zuluaga, backed by popular ex-President Alvaro Uribe, who decimated rebel ranks with a relentless U.S.-backed military onslaught, has been critical of the talks with "terrorists" and drug traffickers.
Santos told Caracol radio that Zuluaga's warming to the idea of talks was hypocritical, branding it "politicking."
"Now it turns out they are friends of peace and for continued negotiations, even though they impose conditions impossible to fulfill," Santos said.
The first voter poll since Sunday's first round, published on Thursday by researcher Cifras y Conceptos, showed Santos had a narrow lead of 1 percentage point over Zuluaga, with 38 and 37 percent of voter intentions, respectively, in a survey of 1,672 respondents.
With a 2.9 percentage point margin of error, the two are technically tied.
Leftist Clara Lopez, of the Democratic Pole party, said late on Thursday that she, like Green Alliance candidate Enrique Penalosa, would not be announcing support for either candidate, though she supports peace talks.
Ex-Conservative candidate Marta Lucia Ramirez, who finished third, announced her support for Zuluaga on Wednesday. (Additional reporting by Luis Jaime Acosta in Bogota; editing by Matthew Lewis and Simon Cameron-Moore)