Retired Dutch General Patrick Cammaert chaired the meeting aboard a UN vessel docked off the coast of the flashpoint city of Hudaida.
Representatives from both sides in the Yemen conflict met on a ship on the Red Sea on Sunday in a UN-led push to implement a stalled troop withdrawal from Yemen's main port of Hudaida as agreed at December peace talks, a UN official told Reuters.
The United Nations is overseeing the implementation of a ceasefire and troop withdrawal accord in Hudaida, the main entry point for most of Yemen's imports, in the hope it will lead to a political solution to the almost four-year war.
Retired Dutch general Patrick Cammaert, head of the UN mission in Yemen, warned the Saudi-backed government and the Houthi 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.
The warring parties were meant to withdraw their forces by January 7 as part of efforts to avert a full-scale assault on Hudaida, but have failed to do so as the Iranian-aligned Houthi group and the government disagree on who should control the city and ports.
Sunday's meeting was the third time the UN-led Redeployment Coordination Committee (RCC) convened since it was formed in December, bringing together the Houthis with the Saudi-backed, internationally recognised Yemeni government and UN mediators.
The talks are to continue on Monday, a UN statement said, describing the meeting as "cordial and constructive."
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.
The parties met on a UN ship because attempts to convene the third meeting in territory held by coalition forces failed because the Houthis were unwilling to cross the frontline, sources have told Reuters.
The first two meetings were held in territory under Houthi control, after which Cammaert shuttled between the two parties.
The vessel picked up a delegation from Yemen's internationally recognised government at an offshore meeting point in the Red Sea before sailing to Hudaida to pick up the Houthi delegation, a UN statement said on Saturday.
The spokesman for the Yemeni government's delegation to the RCC, Sadiq Dweid, told Reuters the committee had discussed Cammaert's proposals for the troop withdrawal at Sunday's meeting.
"The meetings will continue," he said.
Ceasefire largely in place
The truce has largely held in Hudaida, but clashes have increased in recent weeks and the UN Special Envoy for Yemen Martin Griffiths has urged all parties to reduce tensions. Violence has continued in other parts of the country not subject to the deal.
Griffiths' office told Reuters the meeting had begun on Sunday.
The conflict, widely seen in the region as a proxy war between Saudi Arabia and Iran, has been bogged down in a military stalemate for years.
A coalition led by Saudi Arabia and the United Arab Emirates intervened in Yemen in 2015 to try to restore the government of Abd Rabbu Mansour Hadi after it was ousted from power in the capital Sanaa by the Houthis in late 2014.
The Houthis, who say they are enacting a revolution against corruption, control most urban centres in the poorest Arabian Peninsula nation while Hadi's government controls the southern port of Aden and string of coastal towns.
Pope Francis said on Sunday he is following the humanitarian crisis in Yemen with great worry and urged all sides to respect international agreements and ensure food reaches suffering Yemenis.