Ukraine said Sunday its forces were on the defensive against Russian assaults near the eastern city of Kupiansk, while noting gradual progress near the hotspot city of Bakhmut.

"For two days in a row, the enemy has been actively attacking in the Kupiansk sector in the Kharkiv region. We are on the defence," Deputy Defence Minister Ganna Malyar said.

"Fierce battles are going on, and positions... change several times a day," she added.

Ukraine last month began its highly anticipated fightback after stockpiling Western weapons and building up its offensive forces.

It has however admitted difficult battles, and called on allies to provide more long-range arms and artillery.

But Malyar noted Ukrainian forces were "gradually moving forward" near Bakhmut, seized by Russia in May.

"There is a daily advance on the southern flank around Bakhmut. On the northern flank, we are trying to hold our positions, the enemy is attacking," she said.

The city once home to 70,000 people and known for its sparkling wine and salt mine has been destroyed by the longest and bloodiest battle of the war.

"In Bakhmut itself, we are shelling the enemy, and the enemy is shelling us," Malyar said.