Three deaths were reported in early fighting.
Russian President Vladimir Putin's spokesman said the offensive "effectively destroyed the last hope for the implementation of the Geneva agreements" which were intended to defuse the crisis.
Two Ukrainian helicopters were shot down and their pilots killed, both sides said. The Ukrainian Security Service said one of the helicopters was shot down with a surface-to-air missile, which it said undercut Russia's claims that the city is under control of civilians who took up arms.
Putin's spokesman, Dmitry Peskov, said the Kremlin had sent an envoy to Ukraine's southeast to negotiate the release of foreign military observers who were captured by pro-Russian militia in Slovyansk.
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In comments to Russian news agencies, Peskov said the Kremlin has not been able to get in touch with the envoy, Vladimir Lukin, since Ukraine launched the offensive. However, Russia's Interfax and RIA Novosti quoted Lukin's aides as saying he was in touch and safe.
The action came a day after Putin said that Ukraine should withdraw its military from the eastern and southern regions of the country. Russia has massed tens of thousands of troops along the Ukrainian border as it warns Ukraine's military not to move against the insurgents in the east.
Ukraine's acting president, Oleksandr Turchynov, said this week that some troops were "either helping or cooperating with terrorist organizations."
The Ukrainian interior minister, Arsen Avakov, said in a statement that government troops met fierce resistance, but had managed to take control of nine checkpoints on roads around Slovyansk.
Avakov called on the insurgents to lay down the arms and release the hostages they have taken.