Yemeni foreign minister Khaled al-Yamani accused the Houthis of being totally irresponsible and of trying to sabotage the negotiations
Yemen peace talks collapsed on Saturday after three days of waiting for the Houthi movement delegation, but the United Nations envoy vowed to press ahead with diplomacy.
The Houthi's failure to come to Geneva for the first talks in three years was "the elephant in the room", but did not signify the peace process was deadlocked, UN Special Envoy Martin Griffiths said.
Griffiths, who held three days of talks with a Yemeni government delegation, said he would meet in coming days with the Houthi leadership in Sanaa and Muscat, Oman.
"They would have like to get here, we didn't make conditions sufficiently correct to get them here," Griffiths told a news conference, declining to elaborate.
The Houthi group said on Friday it was still waiting for the United Nations to guarantee that the flight carrying its delegation to Geneva would not be inspected by Saudi coalition forces and could evacuate some of its wounded.
Griffiths, referring to peace processes, said on Saturday: "A restart is a very delicate, fragile moment. People are coming at a time when perhaps all of their constituencies are not fully engaged and don't see ahead of time results that will come out of talks.
"So I don't take this as a fundamental blockage in the process," he added.
Confidence-building measures such as prisoner releases, increasing humanitarian access, especially to the city of Taiz, and reopening Sanaa airport were discussed with the government, he said.
Agreement has been reached for medical evacuations from the Houthi-held Yemeni capital of Sanaa, to start in a week with a flight to Cairo, he said, calling it an "early achievement."
A Saudi-led military coalition intervened in Yemen's war against the Houthis in 2015 with the aim of restoring the government of Abd-Rabbu Mansour Hadi. The humanitarian situation has worsened sharply since, putting 8.4 million people on the brink of starvation and ruining the already weak economy.
Yemeni foreign minister Khaled al-Yamani, who led the government delegation, accused the Houthis of being "totally irresponsible" and of "trying to sabotage the negotiations."
"If they were sincere in reaching peace, they should have come, even if we were meeting in separate rooms," he told a separate news conference before leaving the Swiss city.
Yamani also strongly criticized Griffiths, who took over as mediator in February.
"We want the UN to be firmer in bringing the other party to the negotiations," he said.
Anwar Gargash, Minister of State for Foreign Affairs for the United Arab Emirates, a key member of the Saudi-led coalition of Sunni Arab states, tweeted: "Despite the serious setback in Geneva the way forward is still a political solution. What is perhaps clearer now to the international community is the unwillingness of the Houthis to engage in good faith with such a process."