A UN spokesman told AFP that three joint working groups formed last week met today afternoon in an attempt to resume discussion of the key issues.
These include the withdrawal of the Iran-backed Shiite Huthi rebels from areas they occupied in a 2014 offensive, the surrender of weapons, the release of prisoners and detainees and agreeing a political settlement.
The renewed direct talks came a day after mediation by the Kuwaiti foreign minister, ambassadors of the mostly Western 18 countries backing the peace process and UN Special envoy Ismail Ould Cheikh Ahmed.
"The participants in the Kuwait negotiations must reflect the aspirations of the Yemeni people. I am confident that Yemenis want an end to the conflict," Ould Cheikh Ahmed said in a statement.
Direct talks broke off on Saturday with the government delegation complaining of a lack of progress and the Huthi rebels protesting about air raids by the Saudi-led Arab coalition.
A source close to the government delegation said the resumption of direct talks came as a result of international diplomatic pressure on the rebels.
A source close to the rebel delegation said it was due to meet the ambassadors of the 18 countries later today.
Yemen's foreign minister said the talks which began on April 21 have made no headway.
"For the sake of peace, we have accepted all proposals submitted to us in order to progress," said Abdulmalek al-Mikhlafi, who heads the government delegation.
"But after three weeks, we have nothing in our hands because the other party backed down on its commitments," Mikhlafi wrote on Twitter.