Ukraine’s forces looked to consolidate rapid territory gains at the weekend, as Russia carried out revenge attacks on its power infrastructure, causing power cuts across the country.
Officials in Ukraine said targets included water facilities and a thermal power station in Kharkiv.
Mr Zelenskyy described the continuing offensive in the north-east, which Ukraine launched last Tuesday, as a potential breakthrough in the six-month long war.
Defence forces had dislodged the enemy from more than 20 settlements in the past day, according to Ukraine's General Staff.
Thousands of Russian soldiers left ammunition and equipment behind as they fled Izium, which they had been using as a logistics hub.
According to an intelligence update from the UK’s Ministry of Defence (MoD), Ukraine has recaptured territory of at least twice the size of Greater London since Wednesday.
It said Russia had probably ordered the withdrawal of troops from the “entirety of occupied Kharkiv Oblast west of the Oskil River” in the face of Ukrainian advances.
“Isolated pockets of resistance remain in this sector, but since Wednesday, Ukraine has recaptured territory at least twice the size of Greater London.”
Russia is also struggling in the south, near Kherson, to bring sufficient reserves forward across the Dnipro River to the front line, said the MoD.
“An improvised floating bridge Russia started over two weeks ago remains incomplete; Ukrainian long-range artillery is now probably hitting crossings of the Dnipro so frequently that Russia cannot carry out repairs to damaged Road bridges.”
In the village of Kozacha Lopan north of Kharkiv, near the Russian border, Ukrainian soldiers and local officials were greeted by residents with hugs and handshakes.
“Kozacha (Lopan) is and will be Ukraine,” district mayor Vyacheslav Zadorenko said, in a video he posted on Facebook.
“No 'Russian World' whatsoever. See for yourselves where the 'Russian World' rags are lying around. Glory to Ukraine, glory to the Ukrainian Armed Forces.”
Former army chief Lord Dannatt said the Russians have “pretty much turned and fled” from the Kharkiv area of Ukraine, representing a “significant reverse” of their position.
While this is a “great success” for the Ukrainians, he said they continue to need “more and more” western arms and ammunition to be able to “keep the pressure up”.
“We are witnessing some incredible scenes,” he told Sky News.
“Although the Ukrainians have made significant advances, there's a lot of their country still in Russian occupation. So there's a long way to go.”
Speaking on Radio 4 on Monday morning, Sergei Markov, a Russian political scientist and former close adviser to Russian President Vladimir Putin, said “of course” he was concerned by the recent Ukrainian gains.
“It’s a big victory of the Ukrainian army, which took something [like] 5 per cent of the territories which had been taken by the Russian army before,” he said.
Mr Markov said he suspected Russia would now change its strategy, moving towards escalation to “more real war,” which will involve “some kind of mobilisation”.
“Some mobilisation in Russia will happen. Possibly mobilisation of IT specialists. Mobilisation of the special forces, something like this.
“And most important, it could be mobilisation for the Russian economy. Because Russia needs much more drones, much more specific modern weaponry.”
Lord Dannatt said Russia is responding to Ukraine's recent success in the Kharkiv area in a “typically heavy handed way”.
“They know that they've had a significant reverse on the battlefield, so they're lashing out in other ways to try and restore their position,” he told Sky News.
He said targeting a power station was an example of Moscow “blindly lashing out”.
The retaliatory attacks caused a total power cut in the Kharkiv and Donetsk regions, and partial blackouts in the Zaporizhzhia, Dnipropetrovsk and Sumy regions, Mr Zelenskyy said.
Kharkiv governor Oleh Synehubov said 80 per cent of electricity and water supplies had been restored in the region by Monday morning.
An adviser to Mr Zelenskyy admitted on an early morning interview on BBC Radio 4 that Russia may try and win the war by unconventional tactics, taking out power and water and attacking steel and electricity plants.
“They have moved to that strategy months ago when they realised their blitzkrieg had failed,” said Alexander Rodnyansky, who is also an associate professor of economics at the University of Cambridge.
“If you can’t achieve an immediate victory on their end then they are going to try and make this a slow and painful death for us. But they are not going to be successful with that.”
On Sunday, French President Emmanuel Macron called on his Russian counterpart Vladimir Putin to end military operations and come to the negotiating table.
“President Macron had a phone call with his Russian counterpart, Vladimir Putin, and called for ending Russian military operations as soon as possible so that negotiations can begin,” a statement from the Elysee Palace said.
Mr Macron also expressed his concern to the Russian president about the safety of the Zaporizhzhia nuclear power plant.
The head of the International Atomic Energy Agency, Rafael Grossi, said on Monday both sides are interested in the UN atomic watchdog's proposal to establish a protection zone around the Russian-held plant.
Mr Grossi has called both for an immediate stop to nearby shelling, which Ukraine and Russia both blame on each other, and a more formal "nuclear safety and security protection zone" around the plant.
"I have seen signs that they are interested in this agreement," he told a news conference. "What I see is two sides that are engaging with us, that are asking questions, lots of questions."
Issues being discussed include the radius of the zone and the role of IAEA staff, Mr Grossi said. Two IAEA officials are currently stationed at the plant and form what the agency calls a "continuous presence" there.