"We really came here with a big hope ... But unfortunately the Huthi delegation did not allow us really to reach a real progress as we expected," Riad Yassin told reporters.
He stressed though that "not getting a success as we hoped didn't mean that we have failed," adding efforts would continue to find a peaceful solution to Yemen's brutal conflict.
He said the government delegation remained optimistic of a peaceful solution for Yemen "under the umbrella of the UN," but said no date had yet been set for the next round of talks.
The rebels have overrun much of the Sunni-majority country and, along with their allies among forces loyal to ousted president Ali Abdullah Saleh, have been the target of Saudi-led air strikes since March.
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More than 2,600 people have been killed since then.
UN Secretary General Ban Ki-moon launched the high-stakes Geneva negotiations on Monday with an appeal for a two-week humanitarian truce during the holy Muslim month of Ramadan.
But the belligerents' positions have been so far apart that they have not even sat down in the same room, forcing UN special envoy for Yemen Ismail Ould Cheikh Ahmed to shuttle between them for separate consultations.
The rebels meanwhile have demanded an unconditional halt to the air strikes before they consider a pause in fighting.
Ould Cheikh Ahmed was scheduled to host a news conference at the UN in Geneva today afternoon to announce the end of the talks.