UN special envoy Ismail Ould Cheikh Ahmed has held several rounds of talks with Shiite Huthi rebels and a government delegation over the past two days focussing on key issues.
Besides discussing ways to firm up an ongoing ceasefire, delegates also tackled "the issues related to the withdrawal of armed groups, handover of heavy weapons, resumption of the political transition and the release of prisoners and detainees," Ould Cheikh Ahmed said in a statement.
He said a "positive atmosphere" prevailed during talks but warned that differences remained.
"The divergence of views is to be expected in a country witnessing war. It is crucial that all parties make concessions... in order to reach a comprehensive political agreement," he said.
More than 6,800 people have been killed and around 2.8 million displaced in Yemen since a Saudi-led Arab coalition began operations in March 2015 against the Iran-backed Huthis, who have seized swathes of territory including the capital Sanaa.
After the start of the latest round of negotiations was delayed as the rebel delegation sought guarantees, Ould Cheikh Ahmed has managed to get the two sides to approve the agenda and has begun debating key issues.
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Sources close to the negotiations however said the two delegations have not yet met face-to-face.
The government delegation proposed a mechanism on how to implement the withdrawal of the rebels and handover of heavy arms, a Yemeni official said.
"We are optimistic over the prospects of an agreement being worked out by the UN envoy," Mani al-Matari, the press advisor to Yemen's foreign minister, told AFP.
The main sticking point remains that the rebels want to discuss a political settlement before surrendering arms while the government delegation insists on the implementation of UN Security Council resolution 2216.
The resolution states that the rebels must withdraw from seized territories and disarm before talks can progress.
The government delegation also submitted a letter of "strong protest" to the UN envoy over alleged rebel ceasefire violations, especially in third city Taez, Matari said.
Ould Cheikh Ahmed said the negotiations have no timeframe.
The 15-member UN Security Council on Monday stressed the importance of agreeing on a "roadmap" to implement security measures including the withdrawal of heavy weapons from Yemen.