Around 10,000 people have been killed since the coalition intervened in 2015, according to the World Health Organization, although rights groups say the death toll could be five times higher
The head of the United Nations team tasked with monitoring a fragile ceasefire in the flashpoint city of Hodeidah on Monday visited its lifeline docks, a port official said.
Retired Dutch general Patrick Cammaert called on Saudi-backed government forces and Iran-linked Houthi rebels to respect the hard-won truce, Hodeidah port deputy director Yehya Sharafeddin said.
"The (UN) official promised us that the war will end," Sharafeddin told AFP by phone after Cammaert visited the docks, through which the majority of imports and humanitarian aid enter Yemen.
"He said the Yemen war had been forgotten for years but that the international community is now adamant about ending it," Sharafeddin added.
Cammaert later met with local officials in a government building in Hodeidah city.
"We cannot solve your problem, you have to do that yourselves," he told them.
"It is extremely important that both sides are holding that (the ceasefire), and that they don't" blame each other, he added.
Cammaert is heading a joint committee including members of the government and the Houthi rebels, in charge of monitoring the truce in the vital Red Sea city and its surroundings that began on December 18.
Cammaert arrived in Hodeidah from the rebel-held capital Sanaa, after meeting with government officials in Aden.
Yemen's warring sides agreed on the ceasefire to halt a devastating offensive by government forces and an allied Saudi-led coalition against rebel-held Hodeidah at peace talks in Sweden this month.
According to the UN, Cammaert will chair a meeting of the joint committee on Wednesday.
That meeting would be "one of the priorities" of Cammaert's mission, UN spokesman Stephane Dujarric said.
The UN Security Council unanimously approved a resolution authorising the deployment of observers to Hodeidah to monitor the truce.
Port director Sharafeddin said Cammaert "stressed the importance of implementing the agreement" and will visit "battlefronts (in the city) at a later time".
The ceasefire, the result of intense diplomatic efforts led by the UN, has remained shaky with both sides accusing each other of violations in Hodeidah province.
Coalition spokesman Turki al-Maliki said on Monday that the Houthi rebels have violated the truce agreement 138 times since it came into effect.
The latest Security Council resolution on Yemen "puts the Houthi militias under international pressure", he said during a press conference in Riyadh.
The UN monitoring team aims to secure the functioning of Hodeidah port and supervise the withdrawal of fighters from the city.
The text approved by the Security Council "insists on the full respect by all parties of the ceasefire agreed" for Hodeidah.
It authorises the United Nations to "establish and deploy, for an initial period of 30 days from the adoption of this resolution, an advance team to begin monitoring" the ceasefire, under Cammaert's leadership.
Around 10,000 people have been killed since the coalition intervened in 2015, according to the World Health Organization, although rights groups say the death toll could be five times higher.
The conflict has unleashed a major humanitarian crisis and pushed 14 million Yemenis to the brink of famine.