Yemen's rival parties have started face-to-face peace talks on "key issues" in a bid to end the conflict in the country, according to the United Nations.

More than 6,800 people have been killed and about 2.8 million displaced in Yemen since an Arab coalition began operations in March 2015 in defence of the government against Iran-backed Houthi rebels, who seized swaths of territory including the capital Sanaa.

"All delegations are present. Key issues will be addressed," Charbel Raji, spokesman for Yemen's UN envoy Ismail Ould Cheikh Ahmed, told AFP news agency on Saturday about the negotiations taking place in Kuwait.

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Most of the meetings in talks, which began April 21, have so far been confined to encounters between rival delegations and Ould Cheikh Ahmed.

Key issues to navigate include the withdrawal of armed groups, a handover of heavy weapons, the resumption of a political transition and the release of prisoners.

The new phase of meetings comes after the government and rebel delegations each submitted a framework for a political and security solution to end the 13-month war.

No details were available on the content of the proposals, but the government delegation in Kuwait said it is based on implementing UN Security Council Resolution 2216.

The resolution states that the rebels must withdraw from seized territories and disarm before talks can progress.

The rebel-controlled sabanews.net website reported that a "new phase in the negotiations begins Saturday, which would truly test the positions of the UN and international community" in the search for peace.

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Both sides said that they were committed to ensuring the success of the talks in Kuwait, which were preceded by a shaky ceasefire since April 11.

The main sticking point remains that the rebels want to discuss a political settlement before surrendering arms while the government delegation insists that implementing the UN resolution is a priority.

The government delegation on Friday called on the UN envoy to end what it called ceasefire violations by the rebels.

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 Yemeni towns.

Last Sunday, fighter jets targeted the al-Qaeda-held port city of Mukalla and killed 30 fighters, residents said.

The Arab coalition has stepped up an offensive to reclaim parts of the south from the control of Al-Qaeda in the Arabian Peninsula (AQAP).

"The liberation of Mukalla from the hands of the al-Qaeda terrorist organisation has begun," Ahmed Saeed Bin Breik, the governor, said in a statement at the time.