Evo Morales, the Bolivian president, said Hugo Chavez, the Venezuelan president, had already decided to withdraw from the competition and make way for his country to compete for one of Latin America's two-year rotating seats on the council.
But on Tuesday Francisco Arias Cardenas, Venezuela's ambassador to the UN, downplayed those remarks, saying such a scenario was just one possible solution. And Guatemala vowed not to step down in favour of Bolivia.
Cardenas said in a telephone interview: "There are several solutions. One of them is the one President Evo Morales is mentioning. Probably there will be other solutions. But we are exploring solutions, we are exploring ways out."
Chavez has portrayed the contest as a competition between Venezuela and the US because of open US lobbying for Guatemala.
Failure to win the seat on the 15-member Security Council is a major setback to Chavez, who set it as his foreign policy priority this year and wanted to use the council to be a leading anti-US voice on a world stage.
Venezuela failed to win more votes than Guatemala in 35 rounds of voting last week but the tiny Central American nation also lacked the two-thirds majority among UN members to earn the seat.
Cardenas met his Guatemalan counterpart to negotiate a solution before voting is due to resume on Wednesday. He said Venezuela will not step aside if Guatemala remains in the race because that would be conceding victory to the US.
Guatemala says no
Gert Rosenthal, the Guatemalan foreign minister, said Guatemala would not give way to a Bolivian compromise candidacy.
"We have not pulled out and we have no intention of doing so," he said.
Rosenthal said in Guatemala City: "The Bolivia idea was apparently a unilateral decision by Venezuela because they have not notified me".
Typically regions decide by consensus which country will represent them. But the Guatemala-Venezuela contest has divided Latin America and turned into a battle for influence between Washington and Caracas.
Venezuela is a major oil supplier to the US. But relations have deteriorated under Chavez, who describes the superpower as his No 1 enemy and called President George Bush "the devil" in a UN speech last month.
Morales, who also has strained relations with Washington because of his support for Chavez and rejection of US drug policies, said the Venezuelan leader called him to say he would make way for his country to compete for the seat.