A view shows a theatre building destroyed in the course of the Ukraine-Russia conflict in Mariupol, Ukraine. Reuters

Russia struck over 90 military targets in Ukraine overnight, killing at least 500 Ukrainian soldiers and destroying dozens of armoured vehicles, artillery and other military equipment, the defence ministry said.

Russia also said it struck two ammunition depots in Ukraine's eastern Kharkiv region.

Russia's foreign minister told the world not to underestimate the considerable risks of nuclear conflict, and NATO's supply of weapons to Ukraine "in essence" meant that the Western alliance was engaged in a proxy war with Russia.

Russia’s top diplomat also warned Ukraine that his country unleashed attacks against rail and fuel installations far from the front lines of Moscow’s new eastern offensive.

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Interviewed by Russian state television, Foreign Minister Sergei Lavrov was asked about the importance of avoiding World War Three and whether the current situation was comparable to the 1962 Cuban Missile Crisis.

"The risks now are considerable," Lavrov said according to a transcript of the interview on the ministry's website.

Russian Foreign Minister Sergei Lavrov speaks during an event. File photo

"I would not want to elevate those risks artificially. Many would like that. The danger is serious, real. And we must not underestimate it."

The US has been rushing more weaponry to Ukraine and said the assistance from Western allies is making a difference in the 2-month-old war.

"Russia is failing. Ukraine is succeeding,” US Secretary of State Antony Blinken declared Monday after he and the US secretary of defence made a bold visit to Kyiv to meet with President Volodymyr Zelensky.

A local resident sits outside a block of flats heavily damaged during the Ukraine-Russia conflict in Mariupol. Reuters

Blinken said Washington approved a $165 million sale of ammunition — non-US ammo, mainly if not entirely for Ukraine's Soviet-era weapons — and will also provide more than $300 million in financing to buy more supplies.

Ukraine's Foreign Minister Dmytro Kuleba said he regarded Russia's scaremongering as a sign of weakness.

Russia had lost its "last hope to scare the world off supporting Ukraine," Kuleba wrote on Twitter after Lavrov's interview. "This only means Moscow senses defeat."

Meanwhile, the British Defence Ministry said Tuesday that Russian forces had taken the Ukrainian city of Kreminna in the Lukansk region after days of street-to-street fighting.

The debris of a Russian missile used to attack one of the railway facilities in the Lviv region, Ukraine. Reuters

"The city of Kreminna has reportedly fallen and heavy fighting is reported south of Izium as Russian forces attempt to advance towards the cities of Sloviansk and Kramatorsk from the north and east,” the British military said in a tweet. It did not say how it knew the city, 575 kilometres (355 miles) southeast of the Ukrainian capital, Kyiv, had fallen. The Ukrainian government did not immediately comment.

On Monday, Russia focused its firepower elsewhere, with missiles and warplanes striking far behind the front lines to try to thwart Ukrainian supply efforts.

Five railroad stations in central and western Ukraine were hit, and one worker was killed, said Oleksandr Kamyshin, head of Ukraine's state railway. The bombardment included a missile attack near Lviv, the western city near the Polish border that has been swelled by Ukrainians fleeing the violence elsewhere.

Ukrainian authorities said at least five people were killed by Russian strikes in the central Vynnytsia region.