The call came just before the U.N. Security Council met late Saturday morning to discuss the situation in the Arabian Peninsula nation, where Shiite rebels are pitted against external Arab air forces and fighters loyal to Yemen's displaced Sunni president.
A pause was needed especially in and near the southern Yemeni port city of Aden, where intense fighting has happened in the past two weeks, the International Committee of the Red Cross said. Food, water, medical items and personnel need to get into these areas, the group said.
"Otherwise, put starkly, many more people will die. For the wounded, their chances of survival depend on action within hours, not days," Robert Mardini, the ICRC's head of operations in the Near and Middle East, said.
Another Red Cross official said people are running out of food, water and fuel.
"Medical supplies need to be here yesterday. The situation is difficult,"said Marie-Claire Feghali, a spokeswoman for the ICRC who is in the capital, Sanaa. "We need to save the lives that can be saved."
Meanwhile, residents of Sanaa, witnessed the fiercest Saudi strikes since the air assault started last week. Military facilities, including two bases, within the city limits have been targeted, three senior security officials in Sanaa said.
At the Security Council, Russia submitted a draft resolution calling for a halt to the airstrikes that a nine-country regional coalition, led by Saudi Arabia, has been conducting against the rebels in Yemen for more than a week.
The meeting adjourned with no decision announced.
One diplomat said the draft was missing what the envoy called key elements. It doesn't call for the Houthis to stop fighting, and it does not call for political talks between the belligerents, the diplomat told CNN on condition of anonymity.
Yemen has been descending into chaos in the weeks since Houthi rebels -- minority Shiites who have long complained of being marginalized in the majority Sunni country -- forced Yemeni President Abdu Rabu Mansour Hadi from power in January.
The Houthis put Hadi under house arrest when they overtook Sanaa in January. But Hadi escaped in February, fled to Aden and declared himself to still be president.
Houthis and their allies, including those loyal to Hadi's predecessor, then fought Hadi's forces in the Aden area. Hadi fled Aden in late March, ultimately for Saudi Arabia, when the rebels and their military allies advanced on the city.
The conflict prompted Saudi Arabia, a predominately Sunni nation and Yemen's northern neighbor, and other Arab nations to hit the rebels in Yemen with airstrikes.
A Saudi source told CNN that special forces supplied weapons and communication equipment to Yemeni fighters in Aden loyal to Hadi.
The Houthis were retreating from areas in the center of the city, including the presidential palace there, the source said.
The United Nations said Thursday that at least 519 people have been killed in Yemen in the past two weeks. An additional 1,700 have been wounded. Tens of thousands have fled to nearby Somalia and Djibouti.
In Aden alone, fighting has killed 58 people and injured 200 more in the past two days, Yemeni security officials said. At least 24 of the dead were Houthis.
Al Qaeda complicates the situation
Complicating matters in Yemen is that al Qaeda in the Arabian Peninsula -- not the Houthis or Hadi-loyal forces -- holds sway in the country's east. AQAP is considered one of the most ruthless branches of the terrorist organization.
Also late this week, photos circulating on social media purported to show senior al Qaeda leader Khaled Batarfi -- whom Yemeni defense officials said militants busted out of jail on Thursday -- posing in a presidential residence in southern Yemen.
Sunni Islamist fighters freed Batarfi with some 270 prisoners
when they overran the town of al Mukallah.
On Saturday, the French military evacuated 44 people, including some French nationals, from the eastern Yemeni port city of Balhaf.