President Volodymyr Zelensky on Monday said it was "impossible to kill Ukraine" as he hailed the liberation of city of Kherson in a surprise visit.
NATO secretary general Jens Stoltenberg meanwhile cautioned that Ukraine was facing difficult months ahead and Russia's military capability should not be underestimated, despite the takeover of Kherson city.
And US President Joe Biden and his Chinese counterpart Xi Jinping -- a key ally of Vladimir Putin -- agreed in talks Monday that nuclear weapons should never be used, including in Ukraine.
The Ukrainian presidency distributed images of Zelensky singing the national anthem with his hand over his chest as the country's blue and yellow flag was hoisted next to Kherson's main administrative building.
"This is what the Russian Federation did in our country, it showed the whole world that it can kill. But all of us, our armed forces, our National Guard and intelligence (services) have shown that it is impossible to kill Ukraine," Zelensky said.
Russian President Vladimir Putin's spokesman denied, however, that the Ukrainian leader's visit had any impact on the status of the Kherson region, which Moscow formally annexed into Russia at a ceremony last month.
In Kherson, Zelensky said that "the price of this war is high".
"People are injured. A large number of dead. (Russian forces) have left or escaped -- we believe that they have escaped because our army has surrounded the enemy and they were in danger," Zelensky said.
"There were fierce battles, and the result is -- today we are in Kherson region."
- 'Fierce battles' -
Late Sunday, Zelensky said Ukrainian forces found evidence of hundreds of new "war crimes" carried out by Russian occupiers in Kherson.
His subsequent visit came just days after Ukrainian troops entered the city -- the Kherson region's administrative centre -- after Russia pulled back its forces on Friday.
The takeover by Ukrainian troops is the latest in a string of setbacks for the Kremlin, which invaded Ukraine on February 24 hoping for a lightning takeover and to topple the government in days.
But Russian troops failed to capture the capital Kyiv and have since been pushed back from large portions of territory in the south and east.
Still, Stoltenberg said that "the coming months will be difficult" and cautioned that: "we should not make the mistake of underestimating Russia".
"Putin's aim is to leave Ukraine cold and dark this winter," he told a press conference in The Hague after meeting the Dutch foreign and defence ministers.
The city of Kherson was the first major urban hub to fall to Russian forces and the only regional capital Moscow's troops gained control over.
Its recapture opens a gateway for Ukraine to the entire Kherson region, with access to both the Black Sea in the west and the Sea of Azov in the east.
The region was one of four that the Kremlin announced in September were annexed and part of Russia. Russian President Vladimir Putin vowed to use all available means to defend them from Ukrainian forces, hinting at the use of nuclear weapons.
Biden and Xi agreed in talks at the G20 however that nuclear weapons should never be used, including in Ukraine, the White House said.
"President Biden and President Xi reiterated their agreement that a nuclear war should never be fought and can never be won and underscored their opposition to the use or threat of use of nuclear weapons in Ukraine," it said in a statement.
Kremlin spokesman Dmitry Peskov said Monday he would not comment on Zelensky's visit to Kherson but added: "this territory is part of the Russian Federation."
- 'Very scared' -
A self-described partisan in Kherson told AFP after the Russian withdrawal that he and his friends had spent months walking the streets observing the Russians' every move.
"You watch closely and then come home and write it all down. And then you send the information and hide absolutely everything -- phones, papers, clothes, everything," 19-year-old aspiring musician named Volodymyr Timor said.
"We reported everything -- where their equipment and ammunition sites were, where they slept and where they went out drinking," Timor said.
Ukraine's forces could then use the coordinates to target strikes during a counteroffensive that has seen Russia cede roughly half the land it seized in the first weeks of war.
"I was scared," the imposing but soft-spoken guitarist said of the prospect of being caught and possibly killed.
Fuelling concerns that Moscow may have a lingering presence in Kherson, Ukrainian intelligence services said they had detained a Russian military serviceman dressed in civilian clothes.
It said his task was "to gather information, adjust fire on the Ukrainain armed forces and carry out sabotage."
Elsewhere, Ukraine's forces had retaken 12 towns and villages in the eastern region of Lugansk, the military and local officials said Monday.
The eastern industrial region has been held by Russian-supported separatists since 2014 but Kyiv's forces have slowly been clawing back territory there.
But Russia's military also said its forces were making gains in the neighbouring region of Donetsk, capturing the village of Pavlivka, where fighting had caused controversy in Russia.
Last week, soldiers from the Far Eastern 155th Marine Guards Brigade complained about heavy losses in an address to the governor of the Far Eastern region of Primorye, Oleg Kozhemyako.