The meeting was to address problems in implementing an agreement reached in Sweden in December that calls for a ceasefire in rebel-held Hodeida
The head of the UN mission in Yemen warned the Saudi-backed government and the Huthi rebels on Sunday that a seven-week ceasefire in the flashpoint city of Hodeida was fragile and urged them to order their commanders on the ground to uphold the truce.
Retired Dutch general Patrick Cammaert met with government representatives and Huthis aboard a vessel anchored in the port of Hodeida on Sunday for talks aimed at shoring up the ceasefire.
The talks are to continue on Monday, a UN statement said, describing the meeting as "cordial and constructive."
The meeting was to address problems in implementing an agreement reached in Sweden in December that calls for a ceasefire in rebel-held Hodeida, a pullback of forces from the port city, and the opening of humanitarian corridors.
Cammaert "warned the parties about the fragility of the ceasefire and urged them to instruct their commanders on the ground to refrain from any further violations that would jeopardize the Stockholm Agreement and the broader peace process for Yemen," the statement said.
At the Vatican, Pope Francis called for urgent "respect" for the ceasefire accord to allow humanitarian aid through.
"I am following the humanitarian crisis in Yemen with great concern," the pontiff said, before leaving on an historic three-day visit to the United Arab Emirates.
The Red Sea port of Hodeida is the entry point for the bulk of Yemen's imported goods and humanitarian aid, providing a lifeline to millions in the Arab world's poorest country.
This is the third meeting of a joint committee on implementing the deal, which has been hailed as a major step toward ending Yemen's devastating four-year war.
During the talks, the Saudi-backed Yemeni government and the Huthi rebels both "reiterated their commitment to implementing the Hodeida aspects of the Stockholm Agreement," the statement said.
In particular, the sides agreed to work towards finding a solution to give aid workers access to the Red Sea Mills food warehouses in Hodeida.
Red Sea Mills was one of the last positions seized by Saudi and Emirati-backed forces before the truce.
The meetings are being held aboard a UN vessel after the rebels refused to hold talks in government-held areas, an official told AFP on condition of anonymity.
The Saudi-backed government and Iran-supported Huthi rebels have accused each other of violating the ceasefire that went into force on December 18.
Deadlines for the pullback of forces from Hodeida and a prisoner swap have slipped, fuelling worries that the hard-won agreement could unravel.
In a letter sent to the Security Council on Thursday, Saudi Arabia, the United Arab Emirates and the Yemeni government accused the Huthis of violating the ceasefire in Hodeida 970 times.
On Sunday a top Yemeni commander, Major General Saleh al-Zandani, the deputy chief of staff, died from wounds he received last month in a drone attack by Huthi rebels on a military parade at an air base, the information minister said.
Yemen's rebels have been mired in a war with government forces backed since 2015 by a Saudi-led coalition.
The conflict has triggered what the UN calls the world's worst humanitarian crisis, with millions of people at risk of starvation.
The World Health Organization has put the death toll since 2015 at about 10,000 people but rights groups say that figure could be five times higher.