President Volodymyr Zelensky said Ukraine's military had made major, rapid advances against Russian forces in the past week, taking back dozens of towns in regions in the south and east that Russia has declared annexed.
"This week alone, since the Russian pseudo-referendum, dozens of population centres have been liberated. These are in Kherson, Kharkiv, Luhansk and Donetsk regions all together," he said in a Tuesday night address.
Russia moved to annex those regions after holding what it called referendums over several days from Sept 23 – votes that were denounced by Kyiv and Western governments as illegal and coercive.
Russian President Vladimir Putin proclaimed their annexation last Friday.
Zelensky named eight small towns in Kherson in the south as recently having been recaptured. Reuters could not independently verify his statements.
A video released by the Ukraine defence ministry appeared to show the Ukrainian flag being raised over one of those communities, Davydiv Brid, in Kherson.
Ukrainian forces retook several villages in an advance along the strategic Dnipro River on Monday, Ukrainian officials and a Russian-backed leader in the area said.
In the east, Ukrainian forces have been expanding an offensive after capturing the main Russian bastion in the north of Donetsk, the town of Lyman.
Russian forces in the Donetsk and Kherson regions have been forced to retreat in recent days and appear to be struggling to halt an increasingly Western-equipped Ukrainian army.
"In some areas of the front line it was possible to extend the area we hold from between 10 to 20km," the southern Operational Command of the Ukrainian Armed Forces (UAF) said on Wednesday.
Russian forces were destroying their reserves of ammunition and trying to destroy bridges and crossings in order to slow the Ukrainian advance, the UAF said in its daily report.
In Kherson, withdrawing Russian forces were planting mines on "infrastructure facilities" and in homes, it said.
In the past 24 hours, Russia had lost 31 servicemen, more than 40 pieces of equipment, including eight tanks, 26 armoured vehicles, and a large calibre howitzer, it said.
Putin had been expected to sign on Tuesday evening a law formally annexing the four Ukrainian regions. They represent about 18% of Ukraine's territory, and Kyiv and its Western allies annexation say is illegal and will not be recognised.
Russia does not fully control any of the four regions it claims - Donetsk and Luhansk in eastern Ukraine and Zaporizhzhia and Kherson in the south - and the Kremlin has said it had yet to determine the borders of the annexed territory.
Russia has escalated its seven-month war with the annexation drive, a military mobilisation and warnings of a possible recourse to nuclear weapons to protect its territory.
Moscow hopes a "partial mobilisation" it announced two weeks ago can help reverse a series of battlefield setbacks.
Defence Minister Sergei Shoigu was cited by the RIA news agency on Tuesday as saying that Russia had so far called up more than 200,000 reservists out of a planned 300,000 men.
Many Russian men have fled the country rather than fight in Ukraine, however, and Russian lawyers say they are working flat out to advise men who want to avoid being drafted.
Russian defence ministry maps presented on Tuesday appeared to show rapid withdrawals of Russian forces from areas in eastern and southern Ukraine where they have been under severe pressure from the Ukrainian counteroffensive.
The ministry's daily video briefing made no mention of any pullbacks, but on maps used to show the location of purported Russian strikes, the shaded area designating Russian military control was much smaller than the day before.
On the eastern front, Denis Pushilin, the Russia-backed leader in Donetsk, said Russian forces were building a serious line of defence around the city of Kreminna after being pushed back.
UN general assembly to meet
US President Joe Biden told Zelensky in a call that the United States would provide Ukraine with US$625 million in new security assistance, including High Mobility Artillery Rocket System (HIMARS) launchers.
Biden also reiterated that the US would "never recognise" Russia's annexation of Ukrainian territory. Earlier, the European Union also rejected Moscow's "illegal annexation" and urged it to unconditionally withdraw its troops.
Russia's ambassador to the US, Anatoly Antonov, said in a social media post that the US decision to send more military aid to Ukraine posed a threat to Russia's interests and increased the risk of a military clash between Russia and the West.
The UN General Assembly is expected to vote next week on a draft resolution denouncing Russia's action, diplomats said. Russia vetoed a similar resolution in the 15-member Security Council last week.
In a decree on Tuesday, Zelensky formally declared any talks with Putin "impossible", while leaving the door open to talks with Moscow if it got a new leader.
The Kremlin said that what it calls its "special military operation" in Ukraine would not end if Kyiv ruled out talks, adding that it "takes two sides to negotiate".