The UN envoy hailed a "constructive" first full day of Yemen peace talks Friday but called for a halt to air strikes by a Saudi-led coalition and missile fire by Iran-backed rebels.

Ismail Ould Cheikh Ahmed said firming up an April 11 ceasefire was essential to the success of the hard-won peace negotiations in Kuwait.

The United Nations hopes that the negotiations -- which were originally due to begin on Monday -- will end fighting across Yemen that has killed more than 6,800 people and driven 2.8 million from their homes since March last year.

Military sources said that the ceasefire was largely holding on the ground, although clashes were continuing around battleground third city Taez -- where pro-government forces have been under rebel siege for months -- and in the Saudi border province of Jawf.

The negotiations in Kuwait opened on Thursday evening with a session lasting less than two hours following the delayed arrival of representatives of the Shiite Huthi rebels and allied forces loyal to ousted president Ali Abdullah Saleh.

The UN envoy, who spent months getting the warring sides to the negotiating table after a 13-month military intervention led by Saudi Arabia to restore beleaguered President Abedrabbo Mansour Hadi, said Friday's talks had been "very constructive".

"There was a consensus on strengthening the ceasefire and the two sides were committed to the need to achieve peace and that this is the last opportunity," he said.

"The ceasefire is respected between 70 percent to 80 percent all over Yemen," he added.

- 'Fewer breaches' -

Ould Cheikh Ahmed said the rebels complained of continuing air strikes by the Saudi-led coalition while the government side complained of continued ceasefire violations by the rebels.

He said he had contacted Saudi Arabia about the coalition air strikes and they had said the raids were ordered only in response to ceasefire violations by the rebels.

"The ceasefire is respected between 70 percent to 80 percent all over Yemen," he added.

Coalition spokesman Brigadier General Ahmed Assiri said there were fewer breaches of the ceasefire than in previous days.

"Our observations tell us that day by day the number of violations keeps decreasing," he told AFP.

He acknowledged that fighting was continuing in and around Taez.

"Taez is a very difficult city, but I think today (Friday) is better than yesterday or two days before," he said.

Ceasefire monitoring teams with rebel and loyalist representatives have been set up in the most contested areas.

But Assiri said that if violations cannot be resolved "on the ground", the coalition reserves the right to strike.

The coalition intervened in March last year when Hadi fled into exile in Riyadh after the rebels, who overran the capital in September 2014, swept through much of the rest of the country.

With the support of coalition troops and air power, Hadi's loyalists have managed to oust the rebels from second city Aden and neighbouring southern provinces as well as some districts on the Saudi border.

- Jihadist gains -

But the rebels and their allies remain in control of the capital and much of the northern and central highlands, as well as the Red Sea coast.

The violence has allowed Al-Qaeda and its jihadist rival the Islamic State group to make headway, overrunning swathes of southern Yemen and establishing a toehold around Aden -- where the Saudi-backed government is based.

The conflict has stoked tensions between Sunni heavyweight Saudi Arabia and its Shiite rival Iran, which has been accused of smuggling weapons to the rebels.

Previous UN-sponsored peace efforts failed to make any headway, and the last ceasefire in December was repeatedly violated and eventually abandoned by the Arab coalition on January 2.

Diplomats say the rebels are demanding an end to the coalition's air campaign and naval blockade, as well as its ground operations.

They also want UN sanctions against some of their leaders, including Saleh, to be lifted.

UN Security Council Resolution 2216, which is seen as a basis for any peace plan, states that the rebels must withdraw from seized territories and disarm before talks can progress.

But diplomatic sources have said the rebels are demanding a change to the UN initiative, preferring to first agree on a political leadership for Yemen before making military concessions on the ground.

At the opening session on Thursday, Ould Cheikh Ahmed said the UN process "will not necessarily follow a particular sequence".

"Instead, discussions will happen in parallel through working committees that will look into implementation mechanisms of each element, for the sake of reaching one comprehensive agreement that paves the way for a peaceful and orderly transition."