Kyiv has said that the West was on its way to "joint victory" over Moscow after Ukraine said it had wrested back Kherson, the first major urban hub to fall after Russia's invasion on 24 February.
London meanwhile said Russia's "strategic failure" in the strategic Black Sea port city would sow doubt among the Russian public about the point of the war in Ukraine.
"There were very few who believed that Ukraine would survive," Ukrainian Foreign Minister Dmytro Kuleba said as he met US Secretary of State Antony Blinken on the sidelines of a Southeast Asian summit in Cambodia.
"This is coming, and our victory will be our joint victory - a victory of all peace-loving nations across the world."
Mr Blinken hailed the "remarkable courage" of Ukraine's military and people and vowed that US support "will continue for as long as it takes" to defeat Russia.
The humiliating Russian retreat was a huge boost to Ukrainians after months of suffering.
The secretary of Ukraine's National Security and Defence Council, Oleksiy Danilov, said the liberation of all annexed territories was just a matter of time.
"We are not going to put anything on ice," he said. "We are not a freezer."
The Ukrainian national anthem rang out in Kherson's central square as a small crowd sang along while huddled around a bonfire, a video published by Ukraine's parliament on social media showed.
"Special units are already in the city," President Volodymyr Zelensky wrote on Telegram, posting footage in which Ukrainian troops appeared to gather with residents.
About 50 kilometres (30 miles) from Kherson, Andriy Zholob, a commander of a medical unit, said they had been greeted by smiling faces and given "embroidered towels which we display on our vehicles".
"We see children running to meet us and greeting us," Mr Zholob told AFP.
In the nearby region of Mykolaiv, which Russian forces have failed to capture despite months of attacks, governor Vitaliy Kim said the entire region apart from the Kinburn Spit in the south had been returned to Ukrainian control.
In Kherson, Kyiv's forces reconnected the local television network to Ukrainian broadcasters after local media reported that retreating Russian forces blew up the television tower and energy facilities, leaving the city without power.
Russia's defence ministry said "more than 30,000 Russian servicemen, about 5,000 pieces of hardware and military equipment and materiel have been withdrawn".
Kherson's full recapture by Kyiv would be a political and symbolic blow to Putin and open a gateway for Ukraine's forces to the entire Kherson region, with access to both the Black Sea in the west and Sea of Azov in the east.
In Ukraine's capital, the news was met with joy.
Wrapped in flags, popping champagne corks and belting out the Ukrainian national anthem, residents of Kherson living in Kyiv gathered in the city's central Maidan square to celebrate.
"I didn't believe it at first, I thought it was going to take weeks and months, a few hundred metres at a time, and now we see them arrive in Kherson in one day, it's the best surprise," said Artem Lukiv, 41, a Kherson resident living in Kyiv.
The Kremlin meanwhile insisted that Kherson was still part of Russia.
"This is a subject of the Russian Federation. There are no changes in this and there cannot be changes," spokesman Dmitry Peskov told reporters.
A full Ukrainian recapture of the Kherson region would disrupt a vital land bridge for Russia between its mainland and the Crimean peninsula, which Moscow annexed from Ukraine in 2014.
Kherson was one of four regions in Ukraine that Putin claimed to have annexed in September.
White House hails Ukraine's 'extraordinary victory' in Kherson
Meanwhile, the White House has hailed what it said appeared to be an "extraordinary victory" for Ukraine in recapturing the city of Kherson from Russian occupiers.
"It does look as though the Ukrainians have just won an extraordinary victory where the one regional capital that Russia had seized in this war is now back under a Ukrainian flag - and that is quite a remarkable thing," National Security Advisor Jake Sullivan told reporters as he accompanied President Joe Biden to the ASEAN summit.
Mr Sullivan said that the Russian retreat would have "broader strategic implications," including relieving the longer-term threat by Russia to other southern Ukrainian cities such as Odesa.
"It's a big moment and it's due to the incredible tenacity and skill of the Ukrainians, backed by the relentless and united support of the United States and our allies," Mr Sullivan said.
Asked about reports that the Biden administration has started to press President Volodymyr Zelensky to explore negotiations with Moscow, Mr Sullivan said that Russia, not Ukraine, was the side that has to decide whether or not to go to the table.
"This whole notion, I think, in the Western press of 'when's Ukraine going to negotiate?' misses the underlying fundamentals," Mr Sullivan said.
Russia, he added, continues to make "outlandish claims" about its self-declared annexations of Ukrainian lands, even as it retreats from Ukrainian counter-attacks.
"Ultimately, at a 30,000-foot level, Ukraine is the party of peace in this conflict and Russia is the party of war. Russia invaded Ukraine. If Russia chose to stop fighting in Ukraine and left, it would be the end of the war. If Ukraine chose to stop fighting and give up, it would be the end of Ukraine," he said.
"In that context, our position remains the same as it has been and fundamentally is in close consultation and support of President Zelensky."
