A Saudi Arabian-led campaign against Iranian-backed Houthis continues to face heavy criticism after an air strike on a funeral gathering killed up to 140 people.
Over the past two years, the war in Yemen has killed more than 6,800 people.
A Saudi-led multinational coalition is backing the internationally recognised government of President Abed Rabbo Mansour Hadi.
It continues to fight against Shiite Houthi rebels supporting former president Ali Abdullah Saleh.
The war was a key topic at a London meeting between British foreign secretary Boris Johnson, United States secretary of state John Kerry and Saudi and United Arab Emirates officials.
Mr Johnson says the fighting in Yemen remains a cause for international concern and every effort must be made to end it.
"The fatalities that we're seeing there have become, I think, an unacceptable level, and we've had a very good meeting today to discuss the way forward. And one of the things we think is absolutely vital is that there should be a ceasefire and that the UN should lead the way in calling for that ceasefire."
The United States is a long-time ally of Saudi Arabia, providing weaponry and aerial refuelling for the coalition's warplanes.
Iran, which supports the Houthis, has two warships in the Gulf of Aden nearby.
Mr Kerry, who met with Iran's foreign minister in Switzerland over the weekend, says a ceasefire must be implemented in the next few days.
"We are not calling for this in a vacuum. There have been communications to both the Houthi, through various intermediaries, as well as to President Hadi, respectful of his position. But this is the time to implement a ceasefire unconditionally and to move to the negotiating table. But we cannot emphasise enough today the urgency of ending the violence at Yemen, of providing for an opportunity for a political settlement - which is the only way it will be ultimately resolved - and of getting to that table as rapidly as possible. "
The fighting took yet another devastating turn when an air strike killed up to 140 people at a funeral hall in the Yemeni capital Sana'a.
The Saudi-led coalition says it was acting on intelligence that the venue had been full of Houthi rebels.
Human Rights Watch says the bombing constitutes an apparent war crime, adding that remnants of a US-made bomb were found at the site.
Several Yemeni politicians, including Abdel Malak Al-Hajiri, have spoken at a press conference inside what was left of the hall to call for an international investigation.
"In the name of the 16 Yemeni political parties and organisations, we demand the UN Security Council quickly form a committee to investigate clearly and fairly this crime, as well as others."
Saleh al-Sahemi, from Yemen's Youth Development Party, is also demanding answers.
"We condemn the brutal acts of aggression on blameless civilians and on the infrastructure. And the worst is the recent great crime against the hall, which resulted in hundreds of dead and injured in this cowardly and disgraceful act that is contrary to all values and international treaties and international humanitarian laws."
Meanwhile, the United States says one of its naval destroyers has been targeted in an apparent failed missile attack launched from the coast of Yemen into the Red Sea.
Defence officials are still trying to determine exactly what happened.
But, if confirmed, it would be the third time this week the USS Mason has been fired upon in international waters from territory in Yemen controlled by the Houthis.
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