The Houthi group called on Saturday for the formation of a transitional government, for UN supervision on Sana'a Airport, and for the western port city of Hodeida to be a neutral zone.
The Houthi leading negotiator, Mohammed Abdul Salam, called for a transitional government with the participation of all political parties, proposal currently rejected by legitimate government arguing that confidence-building measures should be implemented first, including Houthi disarmament.
Abdul Salam stated that his group "accepts a UN role in Sana'a Airport," as part of efforts to reopen the facility.
Houthi rebels on Friday rejected conditions by Hadi government on reopening the airport controlled by the Iran-backed group and closed by the Saudi-led coalition since 2016.
Earlier on the same day, the Yemeni government proposed to reopen the airport put said one of its conditions was that planes be inspected in Aden or Seiyoun airport under its control.
Reuters quoted Abdul Salam as saying that Hodeida should be announced "neutral zone".
Hadi delegation insists on the legitimate government's inspection on the port to ensure that aids reach civilians.
The western port city of Hodeida, where fierce battles waged early in November, is under Houthi control, along with the Yemeni capital of Sana'a and most populated areas in the north.
According to firsthand sources, the third day of Yemeni peace talks saw the formation of three workgroups consisting of members from both the Yemeni government and Houthi delegations to address key issues.
"First group is tasked with developing a program to implement the release of prisoners as agreed upon," said the sources.
"The second team is tasked with addressing Taiz issue, and the third discussing economy, measures of unifying CBY's functions and depositing revenues from Houthi-controlled areas into Aden-based Central Bank in return for paying wades of civil servants across Yemen."
Houthi negotiator, Abdul Qadir al-Mortadha, stated that prisoner swap implementing measures were discussed with Griffiths' team and the ICRC, including the formation of field team from both sides to pick up bodies at all fronts and to put lists naming prisoners and detainees and present them to the UN on the 9th of December.
"We told the UN envoy's team that we are willing, but we prefer to have direct meetings with other party to further accelerate achievements," the Houthi-run Masiera channel quoted Mortadha as saying.
Yemeni peace talks kicked off on Thursday in Rimbo, some 60 km to the north of the Swedish capital Stockholm, between Yemeni government and Houthi delegations.
The UN envoy for Yemen, Martin Griffiths seeks to bridge gaps between both parties' views by discussing tabled issues with every party separately.
Yemen has been racked by an armed conflict that broke out after the Iran-backed Houthis had ousted the internationally recognized government late in 2014.
The conflict escalated after a Saudi-led coalition intervened militarily in the country in March 2015 to reinstate the government of President Hadi, leaving some tens of thousands killed, hundreds of thousands injured, and 3 million displaced.
The UN Office of Coordinating Humanitarian Affairs (OCHA) has warned that Yemen is on the brink of the world's worst famine in decades.