Earlier this week, WHO said it still had trouble delivering two generators to hospitals in Mariupol, whose health system had been hard hit by the siege.
According to WHO, it has been trying to pre-position supplies closer to the front lines to speed up delivery if a window of opportunity opens.
An eastern city called Lviv will serve as the hub for the delivery of 15 generators to hospitals around Ukraine.
A total of four ships are scheduled to arrive in Kharkiv on Tuesday, while three more are heading to Lugansk and Donetsk, which have seen heavy fighting in east Ukraine.
WHO Europe spokesman Bhanu Bhatnagar told reporters via video link that two more are for Mariupol, also in the east.
"We will only move the generators to their final destinations when we can ensure the safety of our personnel and the precious cargo they are transporting," he said.
"The generators will help meet the minimum energy needs of medical and surgical units of referral hospitals, where power supply is limited or non-existent".
Since Russia invaded on February 24, Mariupol became a symbol of Ukraine's fierce resistance.
"We believe Mariupol's health system faces a difficult future," The UN World Food Programme has pleaded for the unhindered delivery of humanitarian assistance to people trapped in encircled areas of Ukraine.
WFP's emergency coordinator in Ukraine, Jakob Kern, told reporters in Geneva via videolink that more than 100,000 people are unable to leave Mariupol and "are in desperate need of food, water, and other essential supplies."
"In such circumstances, any illness that can usually be treated with medicine becomes a life-threatening situation."
Approximately six million people in Ukraine will require food and cash assistance, according to the WFP.
Thus far, the WHO has delivered 218 metric tonnes of emergency and medical supplies and equipment to Ukraine, of which 142 metric tonnes have reached their intended destinations, mostly in the north and east.
According to the WHO, 147 attacks on healthcare sites in Ukraine have occurred since the Russian invasion, resulting in at least 73 deaths and 52 injuries.