KYIV, Ukraine (AP) - Although Russia claims it has won control of Ukraine’s eastern city of Bakhmut after a grinding nine-month conflict in which tens of thousands of fighters have died, top Ukrainian military leaders say the battle is not over.

Ukrainian officials acknowledge they control only a small part of Bakhmut. Deputy Defense Minister Hanna Maliar said Monday that Ukrainian troops hold some areas in its southwestern outskirts, while fighting continues for the strategic heights in the northern and southern parts of the suburbs.

“The offensive potential of the enemy has been significantly reduced. Huge losses have been inflicted on the enemy. We have gained time for certain actions, which will be revealed later,” Maliar said.

Ukraine says their fighters played a key role in their strategy of exhausting Russian forces. And they say their current positions surrounding Bakhmut will let them strike back inside the 400-year-old city.

“Despite the fact that we now control a small part of Bakhmut, the importance of its defense does not lose its relevance,” said Col.-Gen. Oleksandr Syrskyi, who commands Ukraine’s ground forces. “This gives us the opportunity to enter the city in case of a change in the situation. And it will definitely happen.”

The fog of war made it impossible to confirm the situation inside Bakhmut. Russia’s Defense Ministry said fighters of the Wagner private military contractor, backed by Russian troops, had seized the city. Ukraine President Volodymyr Zelenskyy said the city was not being fully occupied.

In a video posted on Telegram, Wagner head Yevgeny Prigozhin said the city came under complete Russian control about midday Saturday, proclaiming it “completely taken” as he held a Russian flag with a group of at least nine masked fighters in body armor and heavy weapons.

Russian President Vladimir Putin badly needed a victory in Bakhmut, analysts say, especially after a winter offensive by his forces failed to take other cities and towns along the front.

But victory in Bakhmut does not necessarily bring Russia any closer to capturing the Donetsk region - Putin’s stated aim at the start of the invasion. Rather, it opens the way to more grinding battles toward Sloviansk or Kostiantynivka, 12 miles away, said Kateryna Stepanenko, a Russia analyst at the Institute for the Study of War, a U.S.-based think tank.

For Ukraine, the important factor has been the high number of Russian casualties and sapping of their adversary’s morale for the small patch of the 932-mile front line as Ukraine gears up for a major counteroffensive in the 15-month-old war.