More than six weeks of Saudi-led air strikes targeting Shiite rebels in Yemen and ground fighting has killed hundreds of people and forced hundreds of thousands to flee the impoverished country.
UN chief Ban Ki-moon urged a humanitarian pause in the conflict as embattled aid agencies say they desperately need supplies, including fuel to run infrastructure such as hospitals.
"The services still available in the country in terms of health, water, food are quickly disappearing because fuel is no longer being brought into the country," said the UN's Johannes van der Klaauw.
"Without fuel hospitals can't work, ambulances can't go out. You can't have the water system working because water has to be pumped. The telecommunication network risks shutting down," he said.
"This all extremely preoccupying. If something is not done in the next few days in terms of bringing fuel and food into the country, Yemen is going to come to a complete standstill."
US Secretary of State John Kerry told reporters in Sri Lanka it was not inevitable that Yemen would become a failed state, stressing however that Washington was working "very hard" to find a solution.
"We are working hard to secure a negotiated process through the UN which will bring the parties together, Yemenites to negotiate the future of Yemen," he said.
Kerry was speaking a day after the UN Security Council failed to back a Russian appeal for an immediate ceasefire or humanitarian pauses in Yemen.
Diplomats said a draft statement submitted by Russia to a closed-door session of the 15-member council was not rejected out of hand on Friday, but that council members needed time to consider the wording.
The Saudi-led coalition launched the air war on March 26 against Iran-backed Huthi rebels who overran much of the country, forcing President Abedrabbo Mansour Hadi to flee to Riyadh.
