Mauritanian diplomat Ismail Ould Cheikh Ahmed said a ceasefire was a priority after reporting to the Security Council on his failed peace talks in Geneva last week.
"It is imperative for all the parties -- and for me everybody is responsible -- to find a truce," the envoy told reporters.
He called for the ceasefire to take hold before the end of Ramadan on July 17.
"We are one step away from famine," said Ould Cheik Ahmed. "We want to really find a way to lessen the suffering of the population."
Some 80 percent of Yemen's population -- 21 million people -- are in need of humanitarian aid and one million people have been displaced in the fighting, the envoy said.
A recent outbreak of dengue fever and fears that polio will return to the country are compounding concerns about the humanitarian emergency in Yemen.
Yemen slid deeper into turmoil when a Saudi-led coalition launched air strikes in late March to stop an advance by Shiite Huthi rebels who drove the president into exile.
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Saudi Arabia and its Gulf allies are demanding that the Huthis pull back from territory seized in their offensive and that President Abedrabbo Mansour Hadi be restored to power.
The UN envoy said a ceasefire would provide for the withdrawal of militias from the cities and set up a monitoring mechanism to report on possible violations.
Ould Cheikh Ahmed stressed there was no military solution to the conflict and said he would press on with his efforts to achieve a ceasefire and a return to political talks.
No date was announced for a new round of talks, but the envoy is continuing consultations with all sides.
A Security Council diplomat separately said it was essential that Saudi Arabia lift its maritime blockade to allow life-saving supplies to reach Yemen.
"Yemen is so dependent on imports for food, health services, fuel," said the diplomat, who asked not to be named.
"There must be some lifting of this blockade so that ships can get through."
The diplomat also described prospects for a new round of political talks as "bleak."