Donetsk region militia says it is ready for a ceasefire to stop the humanitarian catastrophe deteriorating, the self-proclaimed Republic's prime minister said.

LIVE UPDATES: Kiev's bloody eastern Ukraine campaign

“We hope that the international community will influence the bloodthirsty Kiev government,” Aleksandr Zakharchenko said as cited by RIA Novosti. “But in the case of Ukrainian army aggression continuing, our people’s militia will fight with any balance of forces and in any conditions,” he said.

The self-proclaimed Republic's prime minister confirmed Kiev forces surrounded Donetsk on Saturday. Briefing on the current situation there, he said “there is a humanitarian catastrophe in the city.”

“People are dying in shelling. In the case of a storming of the city, the number of victims will increase. Today there are absolutely no humanitarian corridors. Medicines can’t get into Donetsk and food supplies are running out. Because of the blockade and bombardment, it is impossible to repair the destroyed municipal network,” Zakharchenko said. He added the city has problems with water supplies and power.

The statement comes as the UN voiced serious concerns over the situation in eastern Ukraine.

“Innocent civilians trapped in the fighting continue to lose their lives,” UN Secretary General Ban Ki-moon said on Friday.

Ban promised that the UN will continue to "actively and closely" follow the situation, and if there is further deterioration of the humanitarian situation, or if nationally-led response efforts are not sufficient to meet humanitarian needs, the organization will be "ready to consider additional measures of support."

The UN chief also praised Kiev for handling the situation at this stage "appropriately."

Despite increasing numbers of refugees fleeing to Russia and the continuing fighting in eastern Ukraine, Ukrainian officials deny that the region is on verge of a humanitarian catastrophe.

The eastern Ukrainian city of Lugansk declared a state of humanitarian catastrophe on Tuesday, as there are no medical supplies, electricity, or lighting, as well as a lack of mobile and internet communication. Some 250,000 civilians are unable to leave, a statement on the city council website said.

Read more: Humanitarian catastrophe: Lugansk, E. Ukraine, left with no water, power

Russia's Ambassador to the UN, Vitaly Churkin, is calling for an international humanitarian mission to be launched. Whereas Ukraine’s envoy to UN Yuriy Sergeyev said the situation in eastern Ukraine is manageable by the government, adding that there is no humanitarian crisis.

On August 4, Russia’s Foreign Minister Sergey Lavrov proposed humanitarian convoys, saying that Russia was ready to provide humanitarian assistance to its neighbor “on our own.”

The International Committee of the Red Cross (ICRC) supported the proposal, saying that “the ICRC acknowledges receipt of the offer from the Russian Minister of Foreign Affairs, Sergey Lavrov, about organizing aid convoys to the affected areas in Ukraine.”

Kiev officials claimed a Russian "humanitarian convoy" was stopped from crossing the border on Friday over fears it was an attempt by Moscow to invade Ukraine.

"Supposedly in consultation with the International Committee of the Red Cross in Ukraine, the humanitarian convoy with 'peacekeepers' was meant to enter apparently in order to provoke a full-scale conflict," Valeriy Chaliy, deputy head of Ukrainian President Petro Poroshenko's office said.

Russia has denied Kiev’s claims that Russian military attempted to infiltrate Ukrainian territory.

“We struggle to understand what the Ukrainian side means. There have been no attempts of infiltration by the Russian army,” said President Vladimir Putin’s spokesman, Dmitry Peskov.

The Red Cross, at the same time, also denied allegations the organization was involved in any such "humanitarian convoy."

ICRC spokeswoman Sitara Jabee told AFP that if all sides in the conflict were to agree, the ICRC could potentially receive aid from Russia.

But so far, "nothing has been done," she said.