The Russian foreign ministry's human rights ombudsman's comments came shortly after Moscow state media reported the use of incendiary bombs by Kiev's forces in the blockaded eastern city.
"Ukrainian defence forces and nationalists are using prohibited weapons against Slavyansk civilians, firing on refugees and killing children," Russian ombudsman Konstantin Dolgov tweeted.
"Kiev's humanitarian crimes against (Ukraine's) southeastern residents are multiplying. They must be investigated and the guilty punished," he wrote.
Slavyansk, an industrial city of 120,000, has been at the epicentre of Ukraine's two-month offencive against pro-Russian insurgents in the eastern rustbelt of the ex-Soviet state.
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Incendiary devices are designed to set off fires and were used widely during the Vietnam war and are banned by the UN Convention on Certain Conventional Weapons.
Ukraine's National Guard, a part-volunteer force heavily involved in the eastern campaign, dismissed the incendiary bomb charges as "absurd".
"The National Guard categorically denies this information," its press service said in a statement.