It comes after Ukraine said it had launched a major counter-offensive to re-take the Kherson region.
Vicious battles are raging near Kherson in southern Ukraine after Kyiv announced the launch of a counter-offensive in the region.
It wants to push Russian troops out of Kherson -- captured in the early days of the war -- and back across the Dnipro River.
Ukraine said its forces had destroyed "a number of Russian ammunition depots" and "all major bridges" that allow vehicles to cross the Dnieper.
But Moscow said it had repelled Ukrainian "offensive attempts" in the Kherson region as well as in that of Mykolaiv, further west.
"Due to the failure of the Ukrainian offensive (...) the enemy suffered heavy losses of 1,200 men," said Russia's defence ministry.
Euronews cannot independently verify either of these claims.
In a daily intelligence update, the British Ministry of Defence (MoD) said that Ukrainian armoured forces were continuing to assault Russian troops across several axes in south Ukraine.
Ukraine's troops have pushed "the front line back some distance in places, exploiting relatively thinly held Russian defences," it continued.
In response, Russia will likely attempt to "plug gaps in its defences" with reserve units, including some from the east of Ukraine, the MoD added.
The Insitute for the Study of War said that the Kremlin would "likely exploit the lack of an immediate victory" in Kherson "to misrepresent Ukrainian efforts as failing and to undermine public confidence".
It continued that Ukrainian operational silence on the progress of their counter-offensive may add to this.
Like the MoD, the US-based think tank reported that Ukrainian forces were continuing with "ground assaults and strikes against" Russian forces across the Dnipro River.
"Ukrainian forces made gains on the ground and have begun striking [Russian] pontoon ferries across the river," it added.
Amid the unfolding operation in the south, Russia intensified its attacks on several Ukrainian cities on Tuesday, killing four and injuring 11 civilians in Kharkiv to the northeast of Ukraine.
A spokesperson for Ukraine's Southern Operational Command Vladyslav said on Monday night that Ukraine had launched two air strikes overnight on Russian positions in the occupied towns of Kyselivka, west of Kherson, and Kostyrka, north of the regional capital.
Nazarov said Ukraine had also conducted more than 220 strikes using rockets and artillery against undisclosed targets, adding this included three damaged bridges “to confirm their inoperable status.”
Yesterday Russia's defence ministry claimed that it had "defeated" the Ukrainian offensive, which was carried out on Zelenskyy's personal orders.
Again Euronews cannot independently verify these claims.
It claimed had inflicted "significant" losses on Ukrainian forces, saying it had destroyed scores of tanks and other armoured fighting vehicles.
Located on the Black Sea, Russia seized Kherson city -- which had a pre-war population of 280,000 -- at the start of the war in March.