The United Nations Special Envoy for Yemen Martin Griffiths has discussed issues including prisoners, humanitarian access and the reopening of Sanaa airport with Yemen's Foreign Minister Khaled al-Yamani, a UN spokeswoman said on Friday.
But Griffiths, who began consultations with the Yemen government delegation in Geneva on Thursday, still awaits representatives of the Iranian-allied Houthi movement from the capital Sanaa, UN spokeswoman Alessandra Vellucci said.
"He is still working on getting the Ansarullah delegation to Geneva," she said.
"Since yesterday (Thursday) he has been discussing with them confidence-building measures, including the issue of prisoners, humanitarian access, the re-opening of Sanaaa airport, in addition to economic issues," she said.
The United Nations announced on Thursday that Griffiths was not expected to hold any talks at its Geneva offices on Friday.
Two sources in the government delegation told Reuters on Thursday they had given the international envoy additional time to noon on Friday to persuade the Houthis to come to Geneva.
A Saudi-led coalition intervened in Yemen's war against the Iranian-allied Houthis in 2015 to restore President Abd-Rabbu Mansour Hadi's internationally recognised government. Subsequent peace talks flopped.
Since then the humanitarian situation has worsened sharply, putting 8.4 million people on the brink of starvation and ruining the weak economy.
The United Nations wants the government and the Houthi movement to work towards a deal to end the war, remove foreign forces from Yemen and establish a national unity government.
The Houthis' al-Masirah TV reported on Wednesday that the coalition had prevented their delegation from flying from Sanaa to Geneva.
The Houthis have accused the United Nations of not keeping a promise to transport wounded on the flight.
Hamza al-Kamali, Yemeni deputy minister for youth, told reporters in Geneva on Thursday the flight clearance had been given three days earlier.