KYIV (Reuters) -Ukraine's top military command said on Monday its forces were engaged in heavy battles in frontline hot spots, as the defence ministry said several villages were liberated from Russian occupation in the opening phase of a counteroffensive.

Some 25 battles had taken place over the past day near the eastern town of Bakhmut, and further south near Avdiivka and Maryinka, all in the Donetsk region, but also near Bilohorivka in the Luhansk region, Ukraine's armed forces general staff said.

Ukraine's Deputy Defence Minister Hanna Maliar posted on Monday a photo showing soldiers hoisting the Ukrainian flag at what she said was the village of Storozheve in Donetsk, and thanked the 35th Separate Brigade of Marines for liberating it.

Reuters could not verify the report and it was not immediately clear when the village was reclaimed.

On Sunday, Ukraine said its troops had made advances on three villages in Donetsk: Blahodatne, Neskuchne and Makarivka. Storozheve is located between Blahodatne and Neskuchne.

There was no immediate comment from Russian officials.

Some prominent Russian military bloggers indicated that while Ukrainian forces took Blahodatne and Neskuchne, fighting for Makarivka was going on.

Both sides have said their forces had inflicted heavy personnel and equipment losses on their enemy over the past week, as Ukraine's counteroffensive began to take shape.

Russian President Vladimir Putin said on Friday that Ukraine had failed to breach Russian defences, while his defence ministry said it had destroyed several Leopard battle tanks and other equipment that Ukraine had received from the West.

While staying largely silent over the past week about its counteroffensive, Ukraine's military has reported daily battlefield successes.

"Over the last week in the Bakhmut direction, the Russian invaders suffered significant losses," the general staff said on Monday.

The governor of the Donetsk region in Ukraine said one civilian was killed and two were wounded by Russian fire in the Avdiivka region on Sunday.

Ukrainian Defence Minister Oleksii Reznikov said that Kyiv wanted to discuss details of the "aircraft coalition" with its allies at the next meeting of the Ukraine Defence Contact Group on June 15 in Brussels.

Zelenskiy has long been appealing for Ukraine to be supplied with U.S.-made F-16 fighter jets, and for Ukrainian pilots to be trained.

"At this stage, we are talking about training of pilots ... and our technicians and engineers," Ukraine's Military Media Centre quoted Reznikov as saying.

(Reporting by Pavel Polityuk in Kyiv, Anna Pruchnicka in Gdansk and Lidia Kelly in Melbourne; editing by Robert Birsel & Simon Cameron-Moore)