Yemen's warring parties, Houthis allied to Iran and the officially recognized Yemeni government, have promised "unconditional movement" of supplies and medical teams, WHO representative Ahmed shadoul said.
Nineteen trucks pre-loaded with medical supplies were in Aden and Sanaa to start distribution across Yemen. By 1515 GMT (10.15 a.m. EDT), 14 of the trucks had been able to move and some of them had already reached their destinations, WHO spokesman Tarik Jasarevic told Reuters.
About 5 million children are to be vaccinated against crippling polio in a national immunization campaign set for Dec. 19-23, said Shadoul.
"It is estimated that around 80 percent of the population in Yemen are in need of humanitarian assistance. We believe that about 15 million don't have access to proper healthcare," Shadoul told a news briefing in Geneva.
"The needs are huge and the challenges are great."
A ceasefire took effect in Yemen on Tuesday as parties to the civil war started U.N.-sponsored peace talks in Switzerland in a new push to end months of fighting that have killed nearly 6,000 people, a U.N. spokesman said.
Some 150 metric tonnes of supplies in WHO's warehouse in Djibouti are expected to be shipped to Sanaa on Dec. 21 or 22, Shadoul said. From there, ships will take them to other Yemeni ports.
"It depends on access, we may plan more if access is really granted. This is just a test," he said.
Access to Yemen and within the country has been problematic for goods, including for medical supplies, while fuel for hospitals and transport is sorely lacking, he said.
A Saudi-led coalition supporting President Abd-Rabbu Mansour Hadi has carried out air strikes on Yemen since March, after the Houthis seized control of much of the country. Commercial and aid ships must obtain clearance from the alliance's warships to enter Yemeni ports.
"This is a huge issue … We are still having problems with drugs related to dialysis, related to chronic diseases like hypertension and diabetes," Shadoul said.
Some 2.5 million people are displaced within Yemen, and "almost 240,000 vulnerable civilians are living under a virtual state of siege" in Taiz, a WHO statement said.
"We are also intending to send oxygen and trauma kits to Taiz which has been suffering for the last few weeks," Shadoul said.
"With the upcoming winter we are also quite concerned about outbreaks of acute respiratory infections and pneumonia in children," he said.
Outbreaks of measles and meningitis were feared.
Acute malnutrition rates are high among Yemeni children and women, leaving them at risk of dying from such diseases.
"And definitely in the areas which were hit by cyclones, outbreaks of malaria and dengue will come," Shadoul said.
Yemen was hit by two rare cyclones in early November.