The polls on Wednesday mean that a total of 41 votes have now failed to reach a two-thirds consensus on who should fill the seat being vacated by Argentina on January 1.
Such is the impasse that Haya Rashed Al Khalifa, the current assembly president, has said the body will vote only twice a week from now on, setting October 31 and November 1 for the next votes.
Diplomats say Venezuela and Guatemala have agreed in principal to end their contest for one of the two seats earmarked for Latin America on the 15-nation council, but have yet to decide on an alternate candidate.
The Venezuelan and Guatemalan foreign ministers intend to meet in New York on Thursday to try to agree on a consensus candidate for the seat.
Bolivian thumbs up
Guatemala has the strong backing of the US and has won all but one of the votes but has not been able to top the required two-thirds threshold.
The new developments emerged during a meeting of the 35 Latin American and Caribbean UN members.
Ronaldo Sardenberg, the Brazilian ambassador, told reporters: "They accept in principal that they will withdraw their candidacies. But they are not set on a third country."
Names of new candidates did not come up at the closed-door meeting, but Hugo Chavez, the Venezuelan president, said his ally Bolivia would be a good compromise.
Chavez told a women's meeting in Caracas: "I and the people of Venezuela would feel worthily represented by comrade [president] Evo Morales and the people of Bolivia, who are a brother nation."
Chavez has portrayed the contest as a competition with the United States because of open US lobbying for Guatemala, and has boasted of a moral victory in blocking Washington's choice.
The Security Council is made up of 15 members, five of whom are veto-wielding and permanent - Britain, China, France, Russia and the US. The remaining 10 are non-permanent, and five are replaced every year.
The four other member states to assume seats in January were approved without dispute earlier this month.