Casualties on both sides mounted as fierce fighting raged for control of the center of Bakhmut in eastern Ukraine on Monday, Russian and Ukrainian forces said.

Ukraine said that Russia's Wagner mercenary group, which has claimed to be leading Moscow's charge for the industrial city, was pushing forward.

The city that has been the epicenter of fighting for months, making it the longest-running and bloodiest battle of Moscow's invasion.

"Wagner assault units are advancing from several directions, trying to break through our troops' defensive positions and move to the center of the city," the Ukrainian military said in a morning briefing.

"In fierce battles, our defenders are inflicting significant losses on the enemy," it added.

Analysts are divided over the strategic significance of Bakhmut as a military prize but the city has gained important political stature, with both sides pouring significant resources into the fight.

Wagner head Yevgeny Prigozhin also acknowledged that his forces were coming up against determined resistance as they sought to wrest control of the city's center.

"The situation in Bakhmut is difficult, very difficult. The enemy is battling for every meter," Prigozhin said in a post on social media.

"The closer we are to the city center, the more difficult the battles get and the more artillery there is ... Ukrainians are throwing endless reserves (at the fight)," Prigozhin said.

Ukraine has said its strategy with the defense of Bakhmut is to degrade Russia's ability to launch any further offensive in the coming months and buy time to ready its bid to recapture ground.

'Surge' in arms demand

Kyiv has cautioned the city's fall would give Russian forces a clear path deeper into the Donetsk region, which the Kremlin claimed to have annexed into Russia last year.

Russia has reported painstaking gains around Bakhmut in recent weeks, making progress on encircling the city, but it has not made significant territorial gains in months.

The capture of the city would provide the Kremlin with a military win to sell to its domestic audience.

NATO warned last week that Bakhmut could fall within a matter of days while Ukraine leader Volodymyr Zelenskyy has vowed to continue to hold the city "as long as possible."

Russia's invasion of Ukraine, now more than a year old, has seen arms imports into Europe almost double in 2022, driven by massive shipments to Kyiv, which has become the world's third-largest arms destination, researchers said Monday.

"The invasion has really caused a significant surge in demand for arms in Europe, which will have a further effect and most likely will lead to increased arms imports by European states," Pieter Wezeman, a senior researcher at the Stockholm International Peace Research Institute (SIPRI), told AFP.

Russia's attack has had "devastating" consequences for children in residential institutions, with thousands transferred to occupied territories or to Russia, Human Rights Watch also said Monday.

"This brutal war has starkly shown the need to end the perils faced by children who were institutionalized," said Bill Van Esveld, associate children's rights director at the New York-based organization.

At least several thousand children have been transferred to Russia or occupied territories, the report said.