The Latin American and Caribbean group failed to break the impasse over one non-permanent UN Security Council seat from the region with both Guatemala and Venezuela refusing to withdraw or consider a third candidate.
The representatives of 32 countries including the two contestants met on Wednesday but diplomats reported little process.
The 192-member General Assembly will on Thursday resume the voting process which was suspended for 24 hours after 22 rounds failed to produce a result to enable the group to come to some consensus.
A diplomat said Guatemala and Venezuela need some more time before considering the option of withdrawing in favour of a third candidate.
Except in one round, Guatemala has consistently got around 30 more votes than Venezuela but failed get two-thirds majority needed to be elected for a two-year term beginning on January 1.
After unsuccessful discussion among 32 Latin American and Caribbean countries, Guatemalan Foreign Minister Gert Rosenthal, who is personally leading his country's delegation, said his country does not want to paralyse the Assembly but in the absence of a consensus, why not allow the country getting higher number votes to be elected.