The UN envoy to Yemen has expressed frustration at the stagnant peace process as international pressure mounts on the warring sides to reach an agreement to end the war.

Martin Griffiths concluded a round of talks in Saudi Arabia, which is hosting members of Yemen’s internationally recognised government, and in the Yemeni capital of Sanaa, which the Houthi rebels seized after ousting the government in 2014.

“Nobody can be more frustrated than I am," Mr Griffiths said during a press conference in rebel-held Sanaa on Monday night.

“We have spent a year and a half on things which are relatively simple to describe – the ceasefire, the opening of Sanaa Airport, the opening of Hodeidah ports, the much-delayed start of the political negotiations,” he said after meeting with Houthi officials in the capital without announcing any breakthroughs.

Yemen’s six-year-long war started when the Iran-backed rebels ousted the country’s government from the capital in 2014, saying they were fighting a corrupt system and foreign meddling.

A Saudi Arabia-led military coalition intervened the following year at the request of the government to help retake the country from the Iran backed group.

"Throughout the process, we have suggested several ways to bridge the gap between the parties," Mr Griffiths said.

International efforts have been mounting to reach a peace deal in Yemen following talks between officials from Iran and Saudi Arabia last month.

It was their first high-level meeting in Baghdad since Riyadh cut diplomatic ties with Tehran in 2016.

"There's an extraordinary amount of diplomatic consensus ... there is a real diplomatic energy now, which hasn't always been the case," said the envoy.

The rebels are demanding the reopening of Sanaa airport before the implementation of a ceasefire deal as the UN and Washington push for an end to the war.

"All of our proposals have also guaranteed the reopening of this airport where we are speaking today, Sanaa airport," Mr Griffiths said.

Prior to landing in Sanaa, Mr Griffiths held talks with Yemeni and Saudi officials in Saudi Arabia and Oman as he shuttled between interlocutors in a bid to get backing to reopen Sanaa airport, ensure an uninterrupted flow of fuel and commodities through Hodeida ports, and relaunch the political process.

The UN official’s comments came as Yemen’s President Abdrabu Mansur Hadi said on Monday that the Iran-backed rebels have yet to uphold their end of a deal over the situation in Hodeida reached in Sweden in 2018.

“The rebels and those supporting them do not believe in peace,” Mr Hadi told the Swedish Foreign Minister Ann Linde and Sweden’s envoy to Yemen Peter Semneby in Riyadh.

“The Houthis have not implemented the Stockholm Agreement but have taken advantage of the truce to destabilise international maritime system by setting booby-trapped boats, and other violations," he said.

Sweden hosted peace talks in Stockholm in late 2018 that led to a deal based on confidence-building measures that would pave the way towards a political solution to end the conflict.

The deal halted the government offensive to capture Hodeida from the rebels in exchange for all sides pulling forces from the city of over 1 million people and handing over the workings of the vital ports to a neutral local force under the oversight of UN agencies.

The port is vital as over 70 per cent of Yemen's imported goods and the bulk of humanitarian aid enters through the city.

While the offensive was called off after the deal and troops were pulled back after some brief skirmishes, the rebels have yet to hand over the ports or implement other aspects of the deal.

The government says the rebels have used the fact that the deal removed the threat of a government offensive to redeploy elite troops to other front lines. They say this has led to a sharp rise in fighting elsewhere in Yemen.

Mr Hadi said efforts made to reach a peace deal have been rejected by the rebels.