Russian President Vladimir Putin has called for calm in the eastern Ukraine region after Ukrainian forces resorted to heavy shelling against pro-Russian separatists to recapture seized territories.

In a message to his Ukrainian counterpart Petro Poroshenko, the Russian leader said: "I suggest that both parties - the Ukrainian military and Donbass, DPR and LPR [Donetsk and Lugansk People's Republics, respectively] take urgent measures to stop shelling each other's positions and pull out weapons of over 100m calibre," according to Moscow's Channel One television.

Putin said Russia would help ease the situation and called for both sides to implement the Minsk deal, agreed by all the parties including Kiev, pro-Russian separatists and a Moscow delegation.

"We are ready to organise, jointly with the OSCE [Organisation for Security and Co-operation in Europe], control over the realisation of these steps," he said.

Tensions rose in eastern Ukraine's Donbass region after Ukrainian forces launched an operation to retake the territories captured by anti-Ukraine rebels.

Ukrainian authorities have also claimed to have retaken the key Donetsk airport following some of the fiercest fighting in recent months.

Ukraine claims two children were killed by shelling by rebel forces, although this has not been independently verified.

The latest fighting has broken out as Poroshenko pledged to retake all the territories seized by the pro-Russian rebels in the last several months.

"Tens of thousands of people gathered today at the Ukrainian Independence Square. Millions of people throughout Ukraine – from Transcarathia to Lugansk and Donetsk regions – gathered today at the common prayer for the repose of the innocent victims," said Poroshenko during a march to pay respects to the victims of the conflict.

"We will not give up a single inch of the Ukrainian land, we will refund the Donbass. We will resume in the Donbas Ukrainians, and we will demonstrate that another crucial factor in our victory is our unity with you. Now Ukraine is united as never before."