"Innocent civilians trapped in the fighting continue to lose their lives," said a statement issued here by Ban's spokesperson. "The number of those who are fleeing the area continues to grow."
"Restoring vital infrastructure, not least for water and sanitation, is essential for a return to normal life," the statement said.
Ban said that the United Nations has mobilized quickly, in coordination with key humanitarian actors on the ground, to assist government-led efforts to respond effectively to the emerging needs. "We continue to scale up our preparedness and stand ready to increase our support to Ukrainian relief efforts, as required."
The UN chief will continue to actively and closely follow the situation, according to the statement. "If there is further deterioration of the humanitarian situation, or if nationally-led response efforts are not sufficient to meet humanitarian needs, the UN is ready to consider additional measures of support."
"At this stage, the situation is being handled appropriately by the government of Ukraine, in coordination with international partners," the statement added.
The UN chief also appealed to all parties to redouble their efforts toward achieving a lasting and peaceful political solution to the conflict in eastern Ukraine, adding "this is the most effective way to save lives and avoid a humanitarian crisis."
Since fighting flared in mid-April, more than 1,543 people have been killed in the east of the country, including civilians, the military and members of the armed groups, according to the UN Human Rights Monitoring Mission in Ukraine and the World Health Organization (WHO). Some 4,396 have been confirmed wounded but the real number is likely to be much higher.
The UN refugee agency (UNHCR) estimates that more than 15,200 people have left Crimea, while tens of thousands of people continue to flee the fighting in the east. The total number of internally displaced persons in Ukraine stands at over 117,910.