A full and comprehensive ceasefire between Ukrainian government forces and pro-Russia separatists has entered into force in eastern Ukraine, opening the prospect of an end to military and civilian casualties, the two sides said on Monday.

Ukrainian, Russian and OSCE negotiators last week agreed on a full ceasefire in eastern Ukraine from Monday, putting on hold the military conflict that has claimed more than 13,000 lives since 2014.

The deal was backed by the presidents of Russia and Ukraine, Vladimir Putin and Volodymyr Zelenskiy, who agreed "the need for an urgent implementation of extra measures to support the ceasefire regime in Donbass."

Zelenskiy has sought to resolve the conflict since his election last year, arranging several prisoner swaps.

"We are talking about the possibility of a real ceasefire on both sides," the head of Ukraine's joint forces operation Volodymyr Kravchenko told a televised briefing.

"The situation is stable and controlled," he added.

On Sunday, Ukraine's defence ministry said in a statement that its forces "stand ready to give a proper rebuff to the enemy in case of violation of the agreements."

The separatists' DNA news agency said on Monday observers "did not record any violations of the ceasefire by the security forces of Kyiv, starting from 00:01 on July 27 this year."

The two countries have a fraught history and tensions have escalated since 2014, when Moscow seized Ukraine's Crimea peninsula and backed the separatists in the east.

Major combat ended with a ceasefire agreed in the Belarus capital Minsk in 2015, but sporadic clashes still regularly kill civilians, Ukrainian soldiers and separatists, though there is now hope this new agreement will put a halt to the conflict for good.