The Ukrainian army says it has made major gains over the last day around Kherson, after Russia said it was withdrawing from the southern city.
Ukrainian troops say they have taken back the key town of Snihurivka, 50km (30 miles) to the north of Kherson.
Kyiv has also claimed big pushes on two fronts near Kherson, including advances of 7km in some places.
Russia says it has started to exit the city - its top gain in the invasion - but the process could take weeks.
Wednesday's announcement was viewed as a major setback for Moscow's war effort, though Ukrainian officials were sceptical - warning that the manoeuvre could be a trap.
There was no immediate evidence of any mass-scale Russian withdrawal from Kherson.
Ukraine's commander-in-chief Valeriy Zaluzhny said on Thursday that he could not confirm or deny the pull-out - but said his own forces had made important advances.
Gen Zaluzhny said his soldiers had driven forward on two fronts on the western bank of the Dnipro river - an area of land which encompasses Kherson - taking control of 12 settlements.
The 7km gains were made "during the past day", he said, as troops advanced along a northern-eastern axis and a separate western axis.
Video footage showed soldiers being greeted by locals in a square, apparently after entering the town of Snihurivka.
Snihurivka sits at a major road junction and is a rail hub for Mykolaiv region, which borders Kherson to the north and west.
The regional administration in Mykolaiv posted on the Telegram messaging app touting "lots of good news today".
It fuelled speculation on Thursday night that Ukrainian troops had reached the outskirts of Kherson itself, after cryptically posting a single letter - "ch" in Ukrainian.
This was taken as a possible clue that troops had reached the suburban village of Chornobayivka.
It was not possible for the BBC to independently verify the details of the latest territorial gains and losses - but the reports come after weeks of steady advances from the Ukrainian military.
Kherson was the first - and only - regional capital to fall into Russian hands after it invaded Ukraine on 24 February.
From late September, it was viewed by the Kremlin as Russian territory - following so-called "referendums" in occupied areas of Ukraine that were widely discredited by the international community.
On Wednesday, Moscow said it was no longer possible to supply the city, saying it would step back from the western bank of the Dnipro - a river which bisects Ukraine.
Notably, Russian President Vladimir Putin did not take part in the televised announcement.
Ukraine's Gen Zaluzhny said Russia was left with no option but to flee, after its supply lines were destroyed and its command systems disrupted.
Later on Thursday, Ukraine's defence minister said it would take Russia at least a week to withdraw and that it was not easy to predict the actions of his enemy.
Jens Stoltenberg, the chief of the Nato military alliance of Western nations, said it was clear Russia was under "heavy pressure" but that it was important to see "how the situation on the ground develops".
The UK defence secretary said Russia appeared to be setting up a defensive line on the other side of the Dnipro river using concrete installations.
Commenting on the withdrawal, Ben Wallace said that "the world shouldn't be grateful for Russia handing back stolen property".
A Ukrainian presidential adviser said it was too early to celebrate - accusing his enemy of wanting to turn Kherson into a "city of death" by leaving mines and plotting to shell it from afar.
That could add to the casualty count of a war which has already killed or injured 100,000 soldiers on each side and 40,000 civilians, according to the latest estimate from a senior US general.
Separately, the US has announced another $400m (£341m) military aid package for Ukraine - including Avenger air defence systems and Hawk missiles.
Ukrainian President Volodymyr Zelensky earlier said he had also discussed defence support from the UK with British Prime Minister Rishi Sunak.
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