Yemen's government and its allies Saudi Arabia and the United Arab Emirates (UAE) asked the United Nations Security Council on Thursday to turn up the pressure on Houthi rebels to uphold a ceasefire deal.

In a letter sent to the council, the three governments accused the Houthis of violating the ceasefire in the port city of Hodeida 970 times since it came into force on December 18.

They asked the council to "impress upon the Houthis, and their Iranian backers, that they will be held responsible if their continued failure to comply... leads to the collapse of the Stockholm agreement," said the letter seen by AFP.

Yemen's government and the Houthis agreed to the ceasefire and a redeployment of forces from Hodeida during UN-brokered talks in Sweden last month.

But deadlines for the pullback of forces and a prisoner swap have slipped, fuelling worries that the Stockholm agreement may be in jeopardy.

UAE minister of state for foreign affairs Anwar Gargash met with UN Secretary-General Antonio Guterres on Thursday to discuss problems in implementing the Stockholm deal.

"We understand that we need to exercise patience, but it can't be infinite," Gargash told reporters after this meeting.

Gargash raised concerns of a flareup on the ground, triggered by a Houthi provocation. "We do not want to launch an offensive" in Hodeida, said the minister.

"What we want is for the UN and the international community to exert influence and to do that work" and create pressure on the Houthis to comply with the ceasefire deal, he said.

The Houthis have accused the Saudi-led coalition of violating its commitments under the Stockholm agreement.

The council met behind closed doors to hear a report from UN envoy Martin Griffiths who has wrapped up a new round of shuttle diplomacy.

Kuwait's UN ambassador said Griffiths is "optimistic" that a ceasefire in Yemen's key port of Hodeida is holding despite some violations and that Yemen's government and Houthi rebels are committed to redeploying their forces from the area.

Mansour Al-Otaibi said Griffiths told the Security Council in a closed-door video briefing on Thursday that there will be a UN-facilitated meeting of government and Houthi representatives in the next few days on a vessel in Hodeida to discuss details on how to implement the redeployment of forces.

He said the council is united in wanting to see the Dec 13 agreement reached in Stockholm fully implemented.

For nearly four years, Yemen's Houthi rebels have been locked in a war with a regional pro-government alliance led by Riyadh. The conflict has triggered what the UN calls the world's worst humanitarian crisis, with millions of people at risk of starvation.