UN Special Envoy to Yemen Martin Griffiths arrived in Sanaa where he began his tour before heading next to Riyadh.
The UN Security Council is expected to hear a report from Griffiths following his trip.
Informed sources said Griffiths is most likely to discuss the file of the second round of consultations, which is expected to be held by the end of this month or early February the latest.
The envoy held a number of meetings in the Houthi-controlled Yemeni capital with officials from the coup militias.
Both parties discussed recent developments in the Yemeni crisis, especially the need to implement the agreements reached in December in the Swedish capital, Stockholm.
“While in Sanaa, the UN envoy will also meet retired Dutch general Patrick Cammaert, who has been appointed by the UN to head the ceasefire and redeployment in Hodeidah,” EPA quoted unnamed sources.
The Redeployment Coordination Committee (RCC) met about 10 days ago and witnessed the Houthi withdrawal.
The United Nations scorned Houthi leaders after that and stressed the need for their commitment to the accord and the application of the redeployment according to an agreed mechanism.
RCC has not made any significant breakthrough until now, according to Yemeni government sources.
Observers said that Griffiths would discuss the Stockholm Accord and its implementation, some mechanisms and technical matters such as the deployment of observers and finding a solution for the issue of the forces who will take over Hodeidah port.
Sources say that other files will also be discussed with the Houthis, most notably the dates and location of the second round of consultations as well as the activation of "confidence building steps" through Sanaa airport files and the economic file.
Notably, Yemen's warring parties agreed earlier last month to withdraw their forces from the Red Sea port city and observe a ceasefire during UN-sponsored talks in Sweden's Stockholm.
