Shelling intensified in the past 24 hours, "in particular in the northernmost regions," according to Oleg Sinegubov, the head of the Kharkiv regional military administration and the Ukrainian president's office.

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No fatalities had been reported but some people had been injured, Sinegubov added.

"On the line of contact in the Kharkiv region, the enemy is mainly focused on defense," Sinegubov said. "Our defenders hold their positions firmly."

Human rights violations

As the battle for control of the northeastern city escalates, Amnesty International has accused Russia of war crimes in Kharkiv.

In a 40-page report published last week, the human rights group documented the alleged use of cluster munitions and other indiscriminate means of artillery.

The report came days after two American volunteers fighting for Ukraine -- who have since been taken into detention by Russian-backed separatists in Donetsk -- went missing on June 9 during a battle north of Kharkiv.