The delegations resumed "talks and started the plenary session," Charbel Raji, spokesman for the UN envoy Ismail Ould Cheikh Ahmed, told AFP without providing further details.
Sources close to the talks said yesterday that the two sides had failed to reach an understanding on the need to firm up a fragile ceasefire in place since April 11.
Ould Cheikh Ahmed acknowledged the negotiations were difficult but expressed hopes for progress.
The delegates had agreed to appoint two officials, one from each side, to make recommendations on how to sustain the ceasefire, he added.
More From This Section
But the two sides differ on priorities for the ceasefire.
The government delegation said overnight that the ceasefire should include opening safe passages to all besieged areas and releasing political prisoners as well as those abducted as part of confidence-building measures.
The Iran-backed Huthis are demanding an immediate halt to air strikes that a Saudi-led coalition has been carrying out since March 2015 in support of President Abedrabbo Mansour Hadi.
This meant that "the path of negotiations under aggression will not be different from previous rounds," Abdulsalam wrote on Facebook, in reference to the two failed rounds held in Switzerland late last year.
The two sides also differ on the way to tackle other central issues.
The government wants the discussions to start with the issue of a Huthi pullout from areas including the capital Sanaa and relinquishing heavy arms and missiles.
The negotiations in Kuwait opened late Thursday after the delayed arrival of representatives of the Huthi rebels and allied forces loyal to ousted president Ali Abdullah Saleh.