Vladimir Putin exhorted Russians to battle in a defiant Victory Day speech on Monday (local time), but was silent about plans for any escalation in Ukraine, despite Western warnings he might use the event in Red Square to order a national mobilisation.

In Ukraine, there was no let-up in fighting, with Kyiv describing a stepped-up Russian offensive in the east and a renewed push by Moscow to defeat the last Ukrainian troops holding out in a steelworks in ruined Mariupol.

Monday's annual Victory Day celebration in Moscow - with the usual parade of ballistic missiles and tanks rumbling across the cobblestones - was easily the most closely watched of its kind since the 1945 defeat of the Nazis that it celebrates.

Western capitals had openly speculated for weeks that Putin was driving his forces to try to achieve something he could describe as victory in time for the symbolic date - and with few gains so far, might instead announce a national call-up for war.

In the end, he did neither, but repeated his assertions that Russian forces in Ukraine were again fighting Nazis.

"You are fighting for the Motherland, for its future, so that no one forgets the lessons of World War Two. So that there is no place in the world for executioners, castigators and Nazis," he said from the tribune outside the Kremlin walls.

Ukraine's President Volodymyr Zelenskiy, in his own speech to mark the day, promised Ukrainians they would defeat the invasion.

"On the Day of Victory over Nazism, we are fighting for a new victory. The road to it is difficult, but we have no doubt that we will win," said Zelenskiy, who toured central Kyiv in plain army garb with his shirt sleeves rolled-up.

In a clear reference to Putin, Zelenskiy added: "The one who is repeating the horrific crimes of Hitler's regime today, following Nazi philosophy, copying everything they did - he is doomed."

'ONLY DISHONOUR, AND SURELY DEFEAT'

The Soviet victory in World War Two has acquired almost religious status in Russia under Putin, who has invoked the memory of the "Great Patriotic War" throughout what he calls a "special military operation" in Ukraine. Western countries consider that a false analogy to justify an unprovoked war of aggression.

"There can be no victory day, only dishonour and surely defeat in Ukraine," said British Defence Secretary Ben Wallace. "He (Putin) must come to terms with how he's lost in the long run, and he's absolutely lost."

After an assault on Kyiv was defeated in March by strong Ukrainian resistance, Russia poured more troops in for a huge new offensive in the east last month. But so far, Russian gains have been slow, and more Western arms are pouring into Ukraine for an expected counter-attacks.

Western experts on the Russian military - many of whom initially predicted a quick Russian victory - now say Moscow could be running out of fresh troops and weapons to keep fighting for much longer.

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A full declaration of war would allow Russia to send conscripts, now officially barred from being deployed. But that would also risk a backlash at home from families afraid of their sons being drafted.

"What rhetoric Putin used in his speech is immaterial. If he didn't declare war, or a general mobilisation, that's what (is) important," tweeted Phillips O'Brien, a professor of strategic studies at Britain's University of St Andrews.

"Without concrete steps to build a new force, Russia can't fight a long war, and the clock starts ticking on the failure of their army in Ukraine."

The war still seems to enjoy strong public support in Russia, where all independent journalism has now been effectively banned, and state television says Russia is defending itself from NATO. But conscription would test that support.

Olga, participating in St Petersburg's "immortal regiment" commemoration march, said she feared for her student son.

"I'm really worried about him. Really. I know many mothers whose sons are now of conscription age ... They're trying to find any way to save their children from going to this war."

'STORMING OPERATIONS'

Ukraine's defence ministry said on Monday Russian forces backed by tanks and artillery were conducting "storming operations" to try to seize the Azovstal steel plant in Mariupol, where hundreds of Ukrainian defenders have been holding out in a city ruined by months of siege. Civilians sheltering in the plant have been evacuated in recent days.

Ukrainian officials said heavy fighting was underway in the country's east, while four high-precision Onyx missiles fired from the Russian-controlled Crimea peninsula had struck the Odesa area in southwestern Ukraine. The governor of Mykolaiv, also in the southwest, said overnight strikes were very heavy.

Just before the troops and tanks paraded in Red Square, Russian satellite television menus were briefly altered to show viewers in Moscow messages condemning the Ukraine war.

"The TV and the authorities are lying. No to war," the messages said.