Talks between Guatemala and Venezuela's foreign ministers have failed to end their countries' bitter contest over a non-permanent UN Security Council seat.
UN rules allow for voting to continue until agreement is reached
Venezuelan Foreign Minister Nicolas Maduro blamed Guatemala for the impasse saying it had shown no interest in agreeing to a compromise candidate.
Guatemala - which Venezuela says is a US proxy - maintains it has no reason to withdraw as it has led the voting.
The row has become a new focus for tensions between Venezuela and the US.
Washington accuses Caracas of being too confrontational to merit a seat on the council.
Venezuela has meanwhile accused the US of the "crude blackmail" of other nations as it tries to secure a seat for its favoured candidate.
Guatemalan Foreign Minister Gert Rosentahl told the BBC's World Today that his country had no reason to withdraw as it has come out ahead in all but one of the 41 voting rounds.
"We think there are merits in our candidacy, and we think it is very unfair that we have to be the victim of Venezuela's exit strategy.
"Venezuela needs to withdraw because they clearly can not win," Mr Rosentahl said.
Guatemala has already rejected Bolivia, a Venezuelan ally, as a compromise candidate.
Venezuela's ambassador to the UN, Francisco Arias Cardenas, told the BBC that his country was "willing to help break this deadlock which was created by the United States and its bullying of UN member states to accept Guatemala and block Venezuela".
Another possible compromise candidate could be Costa Rica, Mr Arias Cardenas said.
The UN General Assembly has been voting since Monday last week to choose between Guatemala and Venezuela. Voting is expected to resume on Tuesday in New York.
Guatemala has consistently gathered more support in 41 rounds of voting, but neither side has got the two-thirds majority needed in the 192-member General Assembly.
UN rules allow for voting to continue indefinitely until agreement is reached.
A 1979 battle between Cuba and Colombia took three months of voting to resolve, with Mexico eventually emerging as the compromise candidate.
Five of the UN Security Council seats are held permanently by China, the US, Russia, the UK and France.
The others are held by regional blocs from Africa, Latin America, Asia, Western Europe and Eastern Europe.
Other regional seats, which are rotated every two years, went to Indonesia, South Africa, Italy and Belgium in the first round of voting.