"The defensive operation in this area is of crucial strategic importance to deterring the enemy. It is key to the stability of the defence of the entire front," said Ukraine's most senior military official, Valery Zaluzhny.

Ukraine's defence of the city is becoming precarious, with Russian ground forces led by the Wagner mercenary group reporting gains that signal the city could soon be encircled.

But President Volodymyr Zelensky's office said in a statement Tuesday that the Ukrainian leader had met with senior military commanders and agreed his forces should remain in the embattled city.

"Having reviewed the course of the defensive operation in the Bakhmut sector, all members of the (Supreme Commander-in-Chief's) Staff expressed a common position on further holding and defending Bakhmut," his office said in a statement.

Analysts have played down the strategic significance of Bakhmut as a military prize but the city has gained important political stature, with both sides pouring resources into the fight.

The city, which had an estimated pre-war population of some 70,000 people remains an important urban hub in the Donetsk region, which the Kremlin claimed to have annexed last year despite not fully controlling.

The Russian-installed head of the Donetsk region, Denis Pushilin, told journalists Tuesday that "fierce battles" were raging "for every metre" of Bakhmut.

"The Ukrainian regime absolutely does not take into account numerous losses," he said.

The head of the Wagner group that has claimed to be leading Russia's assault on Bakhmut meanwhile said that Ukraine was consolidating forces for a counter-attack.

"They are absolutely preparing," Yevgeny Prigozhin said in a statement on social media, outlining what he said were Kyiv's plans to beat back his troops encircling the city.