* Death penalty move comes amid reports of desertions, defections
* Separatists worried over looting, lawlessness, by fighters
By Thomas Grove
DONETSK, Ukraine, Aug 18 (Reuters) - 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.
"It is no secret that we have service personnel who carry out crimes. There are instances of looting and use of violence," Eduard Yakubovsky, the rebel republic's acting prosecutor-general, said in a video released by the rebels.
Witnesses in Donetsk say armed men have walked into car showrooms and simply driven off with the stock and firearms store owners have been forced to give up their stocks after rebels have demanded arms at gunpoint.
Rebels fear acts such as this are discrediting the separatist cause even as the leadership steps up a recruitment drive to try to hold back government forces.
In an announcement carried on its website, the leadership quoted top officials as expressing anger at looting and "unauthorised" use of force by some of its fighters against the civilian population.
Military tribunals would be set up and a criminal code which included the death penalty for a range of what it called very serious crimes including espionage, subversion and desertion, would be adopted, it said.
"The death penalty in this code will be for the following crimes. First, aggravated murder - that is the murder of two or more people, or with distinct cruelty, or of a child or a pregnant woman, and a range of other crimes," Yakubovsky said in the video, which showed him addressing a leadership meeting.
"Secondly, (it will be handed out) for certain military crimes committed in war times on the battlefield, such as handing over military hardware or weapons, desertion and some others," he said at the meeting on Sunday.
Rebel commander and Muscovite Igor Strelkov, who has since left his post, had previously ordered executions of those in his ranks who were known to have breaken the law while he was leading separatist forces in Slaviansk.
Sections of a criminal code published with the announcement on Monday said treason, espionage, attempts on the life of rebel leaders, rebellion, sabotage as well as murder and rape would all qualify for execution.
Alexander Zakharchenko, the new rebel leader in Donetsk, was also quoted on the rebel website as saying: "Servicemen must know what crimes they will be punished for."
"The death sentence is being brought in as a greater measure of social protection," Zakharchenko said at a news conference. "We haven't shot anyone yet."
Ukrainian military spokesman say that the rebels are now panicking and many are deserting or defecting to the Ukrainian side as the government forces makes inroads into rebel-held enclaves in the east, including Donetsk and Luhansk cities.
Zakharchenko said at the weekend however that the rebels had received a boost by securing supplies of fresh heavy military equipment from Russia and 1,200 trained Russian fighters.
"Introducing the death penalty is not revenge, it is the highest degree of social protection," another senior rebel leader, Vladimir Antyufeyev, was quoted as saying. (Writing by Richard Balmforth; editing by Philippa Fletcher)