Under growing pressure from a government offensive, the rebel leadership in Ukraine's battle-torn east warned its fighters on Monday that desertion and betrayal could be met by execution.

The warning appeared to signal a growing concern by the leadership of the self-proclaimed Donetsk People's Republic (DNR) over a breakdown of discipline in the fighting ranks as Kiev's military stepped up its offensive.

Apart from being worried about desertions, which the Kiev military says are now telling on rebel ranks, the separatists are also worried about widespread lawlessness.