The appeal came as fighting intensified in the key rebel-held Red Sea port city of Hodeida, despite growing worldwide pressure to end a conflict that has left the country on the brink of starvation.
Three-quarters of Yemen's 29 million people are food insecure, 1.8 children suffer from malnutrition and 400,000 children under age 5 are in the worst stage of malnutrition - without intervention they might die.
UN diplomats, speaking on condition of anonymity, said Britain was working with the United States on a draft resolution to stop the fighting in Yemen.
Yemeni officials say fighting has escalated around the key port city of Hodeida, with more than 150 combatants killed over the weekend from both the rebel and government-backed side.
Yemen has been at war since March 2015 when Houthis occupied northern Yemen, forcing the government into exile, resulting in a Saudi-led coalition being formed to support the government that has waged a destructive air campaign in the country.
"We call on all parties to get together later this month under the leadership of the United Nations special envoy... and agree on a ceasefire and a road to peace for Yemen", he added.
The port is the entry point for more than 70 per cent of imports into the impoverished country. An estimated 10,000 people have been killed and more than 8 million are at risk of starvation from a looming famine. Some rights groups estimate the toll could be five times higher.
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"This is the first time clashes have reached this point (the university)", one pro-coalition Yemeni military source said.
A pro-government medical source said that mortar shells landed on residential areas and caused casualties among citizens.
Almost three quarters of the country's imports flow through Hodeida, from where they are transported by land to areas further north.
Geert Cappelaere told The Associated Press in an interview from Yemen that recent USA calls for a cease-fire are imperative to ending the almost four-year war, which pits a Saudi-led coalition against Iran-aligned rebels known as Houthis. "Subsequently, coalition air strikes must cease in all populated areas", said Mike Pompeo, US secretary of state, on Wednesday.
UN Secretary-General Antonio Guterres on Friday called for a halt to violence in Yemen to pull the country back from a "precipice" and build momentum toward talks on ending the war.
Mr Griffiths is trying to salvage peace talks that collapsed in September. He said both the internationally-recognized Yemeni government and Houthi rebels "are not enabling us to do our work as fast as we should".
Saudi Arabia and its allies intervened in the war in the following year to bolster Yemeni President Abedrabbo Mansour Hadi whose government fled to the southern city of Aden.