Yemen's government and Houthi rebels have discussed major political and security issues in face-to-face negotiations aimed at bringing an end to 13 months of devastating war, a UN envoy said.

Three joint working groups formed by the United Nations exchanged views on resolving the political and security issues, and the release of prisoners and detainees, said UN envoy Ismail Ould Cheikh Ahmed.

The teams were formed from members of the warring delegations on Wednesday when direct talks resumed following a three-day interruption after the government delegation walked out in protest against the seizure of an army camp by the rebels.

The talks were entering their third week on Thursday but there has yet to be a breakthrough, with delegations trading accusations of violating the ceasefire that took effect on April 11.

"We have learned that ceasefire violations were committed in the past two days and this is a disturbing development," Ould Cheikh Ahmed told a news conference.

He urged those involved in the negotiations not to allow the ceasefire violations to affect the ongoing peace talks.

READ MORE: Yemen Revolution - "Our dream was sold"

He said a joint UN-sponsored ceasefire monitoring committee had been asked to investigate clashes on the ground and submit detailed reports.

Earlier on Thursday, the head of the Yemeni government delegation, Foreign Minister Abdulmalik al-Mekhlafi, demanded action from UN mediators over rebel shelling of besieged third city Taez.

Mekhlafi said his negotiators had submitted proposals to the UN envoy for implementing an April 11 ceasefire in Taez, where loyalist troops have been under rebel siege for months, trapping tens of thousands of civilians.

Aden airport reopens

As the talks got under way in Kuwait City, the airport in Yemen's government-controlled second city of Aden reopened after months of closure owing to security issues.

In Aden, passengers disembarked from a Yemenia plane coming from Jordan on Thursday, marking the first flight in months to reach the country's second biggest city.

The airport has been closed to civilian traffic since early 2015.

It was badly damaged during months of fighting between rebels and pro-government forces, who finally managed last summer to retake Aden with help from a Saudi-led coalition.

Since then Aden has been declared the temporary capital of Yemen.

Airport director Tarek Abdo said the reopening of Aden airport was made possible after security improved in the southern port city.

There has been mounting international pressure to end the Yemen conflict which has killed more than 6,400 people and displaced 2.8 million since March last year.

The hard-won talks opened in Kuwait on April 21 but the first round of face-to-face negotiations was held only on Saturday.

Source: Agencies