Igor Druz told the BBC such "executions" sent an important signal to the rest of the rebel forces.
He also said Ukraine's government was a "terrorist" organisation, committing war crimes against civilians.
Meanwhile, forensic experts are carrying out a second day of work at the site of a crashed Malaysian plane.
Some 70 Dutch and Australian experts are scouring the vast crash site where Malaysia Airlines flight MH17 crashed after reportedly being brought down by a missile.
More than 1,500 people are believed to have been killed in the conflict which erupted in east Ukraine in April, after rebels declared independence from the new government in Kiev.
Russia, which annexed Ukraine's Crimea region in March, has been accused of arming the rebels and has been targeted by US and EU sanctions.
Russia denies the accusations.
Igor Druz is advisor to the rebels' Russian military commander Igor Strelkov, and a senior spokesman for the rebel-held territories of Donetsk region.
He is in charge of the ideology of the eastern Ukrainian rebel movement.
In an interview with the BBC in Donetsk he outlined his vision of the so-called 'state of Novorossia (New Russia)' they hope to build here.
He says he is a strong supporter of Orthodox Christian morality and family values, and opposed to homosexuality.
He hopes to legalise death penalty for the most serious crimes and he is sure that most rebels will support him in this initiative.
Druz told the BBC: "On several occasions, in a state of emergency, we have carried out executions by shooting to prevent chaos. As a result, our troops, the ones who have pulled out of Slavyansk, are highly disciplined."
Slavyansk was a key rebel stronghold before it was recaptured last month by Ukrainian government forces.
Druz said the rebels wanted to establish a socially responsible state that would protect Christian values.
He also said the Ukrainian government was "totally illegitimate".
Druz said: "These people have come to power by committing murders and staging an armed coup. Now they are committing war crimes. They are bombing our cities. They shell cities and then blame it on our fighters. This is nonsense. Why would we shell cities which are under our control?"
Refugees fleeing the fighting in the east have told the BBC they believe the Ukrainian government is shelling residential areas, and complain they had to escape at short notice with no warning from the government.
Work is continuing at the crash site of MH17, which came down on 17 July with the loss of all 298 passengers and crew, while flying from Amsterdam to Kuala Lumpur.
The BBC's Jonathan Beale, at the scene, says local people have come to a cross near the crash site where flowers have been lain in memory of the victims, and a local priest is conducting a memorial service.
The US and Ukraine say pro-Russian rebels probably shot down the plane with a missile supplied from Russia.
The rebels say it could have been brought down by a Ukrainian fighter jet.
Most of those who died were Dutch nationals.
More than 220 coffins have now been sent back to the Netherlands.
On Friday, US President Barack Obama expressed his "deep concern" over the Ukraine crisis in a telephone call to Russian President Vladimir Putin.
Obama later said: "I think that we have done everything that we can to support the Ukrainian government and to deter Russia from moving further into Ukraine. "But short of going to war, there are going to be some constraints in terms of what we can do if Putin and Russia are ignoring what should be their long-term interests."
The Obama administration on Friday also notified Congress it intended to spend $19m (£11m) training the Ukrainian national guard.
Earlier Putin condemned fresh US and EU sanctions.
He called them "counterproductive, causing serious damage to bilateral cooperation and international stability overall".
Source: BBC News Europe