UN envoy Martin Griffiths said he had held "fruitful consultations" with the delegation representing the government of President Abedrabbo Mansour Hadi, but acknowledged he had been unable to convince the rebel delegation to even show up for the talks.
"We didn't manage to get... the delegation from Sanaa to come here," he told reporters.
"We just didn't make it," he said, insisting though that efforts would continue to bring the parties together.
Rebel chief Abdulmalik al-Huthi defended his decision not to send a delegation to Geneva, calling on his supporters to fight and slamming the government as "mercenaries" and "traitors".
"Our choice is steadfastness and resistance to aggression on all fronts," the rebel chief said in his first public statement after the collapse of negotiations.
The talks, meant to be the first meeting between Yemen's warring sides in two years, had been scheduled to formally open Thursday, but the absence of the rebels left Griffiths scrambling to try to save them.
The Iran-backed Huthis, powerful armed tribes locked in a war with Yemen's Saudi-backed government, refused to take off from the rebel-held capital of Sanaa unless the UN met a list of conditions, which included securing a safe return from Geneva for their delegation.
They accused the Saudi-led alliance backing the Hadi government of planning to strand their delegation in Djibouti, where their plane was to make a stop en route to Geneva.
They hinted they feared a repeat of 2016, when 108 days of talks in Kuwait broke down and a rebel delegation was stranded in Oman for three months due to an air blockade.
Complicating things further, fighting flared again on the ground on Friday with government forces attempting to close in on the rebel-held Red Sea port of Hodeida, which had been expected to be one of the main topics of discussion in Geneva.
- 'Appeasing' the rebels? -
Head of the Yemeni government delegation, Foreign Minister Khaled Yamani, charged that the rebels were "trying to sabotage" the negotiations, and slammed them for being "totally irresponsible".
"I believe that their absence from Geneva is part of their panic over losing their grip on areas under their control," he told reporters.
He also harshly criticised Griffiths for "appeasing" the rebels by refusing to lay blame for the failure of the talks squarely on their shoulders.
When asked at Saturday's press conference who was to blame for the stillborn negotiations, Griffiths had insisted that "it's not my job to find fault. It's my job to find agreement".
This enraged Yamani, who said the UN envoy in private conversations had "expressed his dissatisfaction with (the) unjustified position" of the Huthis not to come to Geneva.
"I believe that the (public) words of the Special Envoy... were unfortunately appeasing the coup plotters and giving them excuse," he said, urging the UN to be "firmer".
- No 'fundamental blockage' -
Griffiths, who said earlier this week he believed the Geneva talks would offer a "flickering signal of hope" to the Yemeni people, said on Saturday that his own hope had not faltered.
"A restart is a very delicate, fragile moment” in any negotiations, he said.
"I don't take this as a fundamental blockage in the process."
He hailed "good progress" made in discussions in recent days with the government delegation on so-called confidence-building measures, including issues like prisoner swaps and the reopening of Sanaa airport.
Griffiths said he would be travelling to Muscat and Sanaa over the next few days to lay the groundwork for future talks, but hinted he might initially engage in separate discussions with the two sides.
He said it was "too early to say when the next round of consultations will take place".
Griffiths has been up against difficult odds from the start.
He is the UN's third Yemen envoy since 2014, when Huthis overran the capital and drove Hadi's government into exile, but all previous attempts to resolve the conflict have failed.
Nearly 10,000 people have been killed since Saudi Arabia and its allies intervened on behalf of the government in 2015, triggering what the UN calls the world's worst humanitarian crisis.