Ukrainian authorities say they've captured many Russian prisoners of war, as Kremlin forces hit back with bombardments.
Russia says it has launched "massive strikes" in response to Ukrainian troops' lightning counter-offensive.
Russian bombing has so far killed eight people and wounded 19 in 24 hours in the north-eastern region of Kharkiv and the eastern region of Donetsk, the Ukrainian presidency said.
"The Russian air force, ballistics and artillery are carrying out massive strikes against units of the Ukrainian armed forces in all operational areas," the Russian defence ministry said on Tuesday.
It referred in particular to bombardments near Sloviansk, Konstantinivka and Bakhmut in eastern Ukraine, as well as in the southern regions of Mykolaïv and Zaporijjia and in that of Kharkiv, from where Russian soldiers have almost completely withdrawn in the face of Ukrainian advances.
The Russian offensive launched on 24 February will continue "until the objectives are achieved", the Kremlin had hammered the day before, according to which there are currently "no prospects for negotiations" between the two countries.
Meanwhile, Kyiv says Russian soldiers are committing "up to 200 war crimes per day" which are being uncovered in areas newly liberated by Ukrainian soldiers in the east and north of the country, and that up to 70,000 square kilometres in ten regions have been mined by Russian troops.
For its part, Russia said that the Ukrainian military was carrying out harsh reprisals against civilians in the areas it had retaken in recent days.
"According to our information, there are many punitive actions against the inhabitants of the Kharkiv region, people are being tortured, mistreated," Kremlin spokesman Dmitry Peskov said, adding: "It is revolting."
Zelenskyy says Ukrainian troops have retaken large tracts of land
Ukraine has now recaptured more than 6,000 square kilometres in a lightning war advance that forced Russian troops to make a hasty retreat, said Ukrainian President Volodymyyr Zelenskyy.
The Ukrainians say they've also captured so many Russian prisoners of war that they're running out of space to accommodate them, as troops were surrendering en masse as "they understand the hopelessness of their situation", said a spokesperson for Ukrainian military intelligence.
In a late-night video address, Zelenskyy said "since the beginning of September, our soldiers have already liberated 6,000 square kilometres of Ukrainian territory in the east and south, and we are continuing to advance".
That's an increase from Sunday's figures when Kyiv claimed only 3,000 square kilometres had been retaken.
Blue-and-yellow Ukrainian flags fluttered over newly liberated towns across a wide swath of reclaimed land. The Ukrainian military said it had freed more than 20 settlements in 24 hours.
Now Ukrainian teams are disarming land mines and other unexploded weapons in the recaptured areas and searching for any remaining Russian troops, officials said.
It was not yet clear if the Ukrainian blitz could signal a turning point in the war. Momentum has switched back and forth before, but rarely with such a big and sudden swing.
Russia admits battlefield setbacks
After months of little discernible movement on the battlefield, the momentum has lifted Ukrainian morale and provoked rare public criticism of Russian President Vladimir Putin’s war.
The counteroffensive left the Kremlin struggling for a response to its largest military defeat in Ukraine since Russian forces pulled back from areas near Kyiv after a botched attempt to capture the capital early in the invasion.
The Russian Defense Ministry acknowledged the setback in a map that showed its troops pressed back along a narrow patch of land on the border with Russia - a tacit admission of big Ukrainian gains.
Reports of chaos abounded as Russian troops pulled out.
“The Russians were here in the morning. Then at noon, they suddenly started shouting wildly and began to run away, charging off in tanks and armoured vehicles,” Dmytro Hrushchenko, a resident of recently liberated Zaliznychne, a small town near the eastern front line, told Sky News.
Video taken by the Ukrainian military showed soldiers raising the Ukrainian flag over battle-damaged buildings. In one scene, a fighter wiped his boots on a Russian flag on the ground. Other videos showed Ukrainians inspecting the wreckage of Russian military vehicles, including tanks.
Ukrainian presidential adviser Oleksiy Arestovich did not specify the number of Russian prisoners but said the POWs would be exchanged for Ukrainian service members held by Moscow. Military intelligence spokesman Andrey Yusov said the captured troops included “significant” numbers of Russian officers.
Ukraine’s deputy interior minister accused fleeing Russian forces of burning official documents and concealing bodies in an attempt to cover up rights violations in the areas they controlled until last week.
The mood was jubilant across the country.
In Kharkiv, Ukraine’s second-largest city and the capital of the region where the gains have been made, authorities hailed that power and water had been restored to about 80% of the region's population following Russian attacks on infrastructure that knocked out electricity in many places across Ukraine.
“You are heroes!!!” Kharkiv Mayor Ihor Terekhov wrote on Telegram, referring to crews who restored utilities in Ukraine's second-biggest city. “Thanks to everyone who did everything possible on this most difficult night for Kharkiv to normalize the life of the city as soon as possible.”
State TV criticises war efforts and blame NATO for losses
Meanwhile, in Russia, signs of disarray emerged as Russian military bloggers and other commentators chastised the Kremlin for failing to mobilize more forces and take stronger action against Ukraine.
Russia has continuously stopped short of calling its invasion a war, instead describing it as a “special military operation” and relying on a limited contingent of volunteers instead of a mass mobilization that could spur civil discontent and protest.
Ramzan Kadyrov, the Moscow-backed leader of the Russian region of Chechnya, publicly criticized the Russian Defense Ministry for what he called “mistakes” that made the Ukrainian blitz possible.
Even more notable, such criticism seeped onto state-controlled Russian TV.
“People who convinced President Putin that the operation will be fast and effective ... these people really set up all of us,” Boris Nadezhdin, a former parliament member, said on a talk show on NTV television. “We’re now at the point where we have to understand that it’s absolutely impossible to defeat Ukraine using these resources and colonial war methods.”
Some in Russia blamed Western weapons and fighters for the losses.
“It’s not Ukraine that attacked Izium, but NATO,” read a headline in the state-supported Komsomolskaya Pravda newspaper, referring to one of the areas where Russia said it has withdrawn troops.