Ukraine's military launched assaults to retake rebel-held eastern towns on Thursday in which up to five people were reported killed, a move Russian President Vladimir Putin warned would have "consequences".

The offensive sent international tensions soaring and oil prices up on the prospect of Russia making good on its threat of a massive response in the ex-Soviet republic.

In Slavyansk, a flashpoint eastern Ukrainian town held by rebels since mid-April, armoured military vehicles drove past an abandoned roadblock in flames to take up position.

Shots were heard as a helicopter flew overhead, and the pro-Kremlin rebels ordered all civilians out of the town hall.

"During the clashes, up to five terrorists were eliminated," and three checkpoints destroyed, the interior ministry said in a statement.

Hours later, the armoured vehicles withdrew, leaving the town calm but tense.

The rebels, which the Kiev government and its Western backers believe are controlled and supported by Moscow, have been occupying around 10 towns in Ukraine's east since mid-April.

An international accord reached in Geneva last week was meant to defuse the crisis, but was swiftly dismissed by the rebels.

A brief truce collapsed over the weekend, prompting Ukraine's acting President Oleksandr Turchynov to order a resumption of an "anti-terrorist" offensive to flush the militants out.

Also on Thursday, Ukrainian special forces seized back control of the town hall in the southeastern port city of Mariupol with no casualties, Interior Minister Arsen Avakov said. Separatist sources confirmed the loss of the building in the port city. And an army base in the eastern town of Artemivsk overnight repelled an attack by heavily-armed rebels using machine-guns and grenades, the interior and defense ministries said.

Putin called the armed offensive a crime.

"If Kiev has really begun to use the army against the country's population... that is a very serious crime against its own people," he said.

Russia, which has an estimated 40,000 troops massed on Ukraine's border, has already threatened to respond as it did when it invaded Georgia in 2008 if it sees its interests in Ukraine attacked.

Shortly after Putin spoke, Russia's defence ministry announced new military "exercises" near the border in response to the Ukrainian military operations.