She did not say whether a long awaited counter-offensive had begun.
Separately, Russia's military said it had repelled a new attack in the eastern Donetsk region on Monday.
Bakhmut has for months been at the heart of fierce fighting. It has little strategic value - but is important symbolically both for Kyiv and Moscow.
Monday's claims by Ukraine and Russia have not been independently verified.
In the early hours of Tuesday, air raid sirens were activated for several hours all over Ukraine. In the capital Kyiv, all missiles - more than 20 - were shot down, city officials said citing preliminary information.
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