U.N. Secretary-General Ban Ki-moon voiced alarm Sunday over fierce fighting around the Donetsk airport in eastern Ukraine and called for an immediate end to the violence.

Heavy shelling rocked the city as Ukraine rushed tanks to the frontlines and declared it had pushed back pro-Russian rebels from most of the airport.

Russia voiced deep concern on Sunday over the escalation of fighting in eastern Ukraine and said President Vladimir Putin has written to his Ukrainian counterpart Petro Poroshenko proposing the withdrawal of heavy weaponry from the front line.

"We are extremely concerned about the latest developments. The bombardments of residential areas have resumed in Donetsk and people are dying once more," Putin's spokesman Dmitry Peskov said, according to Russian news agencies.

Ukraine rushed tanks to the front lines and claimed Sunday to have cleared pro-Russian rebels from most of Donetsk airport after days of intense fighting, with heavy shelling shaking the key eastern city.

As fighting wracked the country's war-torn east, thousands of people held a common prayer and peace march in the capital Kiev attended by President Petro Poroshenko, who vowed the country would not yield to rebels he says have been backed by Russian troops and weapons.

Clashes between Ukraine's army and pro-Russian rebels for control of a battered airport intensified Saturday, with explosions and heavy gunfire shaking the area throughout much of the day and at least six more people killed.

The battle for Donetsk airport in eastern Ukraine saw Kiev rush reinforcements to the snowy front lines, while soldiers in the area spoke of some of the worst shelling yet in the nine-month war.

Fighting in eastern Ukraine has killed three soldiers, officials said Saturday, as an upsurge in clashes in recent days between the army and pro-Russian rebels centred around control of a battered airport.

Further battles shook the area around the Donetsk airport on Saturday, with Ukraine's military saying it was defending its positions despite rebel claims that they had taken control of the site.

In his first prominent speech since telling donors last week he was still interested in the White House, the 2012 Republican nominee hinted and quipped about a possible presidential run next year but stopped well short of any announcement.

With the 2016 election cycle clearly underway and Jeb Bush announcing last month that he is actively exploring a presidential bid, Romney suddenly finds himself under political pressure to signal whether he is ready to mount a third campaign to lead the nation, or yield to a new crop of candidates.

The U.N. Security Council will meet next week to discuss the flareup of violence in Ukraine, diplomats said Friday.

A meeting of the 15-member council will be held on Wednesday at the request of Lithuania.

Fierce fighting in eastern Ukraine has wreaked havoc on the health system, with more than five million people affected, the United Nations said on Friday.

The World Health Organization said access to primary, secondary and emergency health services was "critically needed," adding that the health infrastructure was buckling under the humanitarian crisis.

Fierce fighting in east Ukraine has killed at least 11 people over the past 24 hours, officials said Friday, as a new round of violence threatened all-out conflict between government forces and pro-Russian rebels.

A military spokesman reported six soldiers killed and 18 others wounded over the past day, adding that a civilian was left dead in a rebel strike on a checkpoint near Fashchivka in the Lugansk region.

Ukraine on Thursday renewed accusations of a Russian military build up on its border and approved fresh troop mobilizations as a wave of violence threatened all-out conflict in the country's war-torn east.

A national day of mourning was held for 13 people killed on Tuesday when a rocket exploded near a commuter bus traveling towards the Ukrainian city of Donetsk, the worst loss of civilian life since a September truce that only partially halted the violence.