Russia attacked the Ukrainian president's hometown with suicide drones on Sunday, and Ukraine pushed ahead with its counter-offensive after taking back control of Lyman, a strategic eastern city.

Russia's loss of Lyman, which it had been using as a transport and logistics hub, is a new blow to the Kremlin as it seeks to escalate the conflict after Moscow's formal recognition of four Ukrainian regions under Russian control since the early stage of the Russia-Ukraine conflict as Russian territory.

"The Ukrainian flag is already in Lyman," Ukrainian President Volodymyr Zelenskyy said in his nightly address. "Over the past week, there have been more Ukrainian flags in the Donbas. In a week there will be even more."

A ceremony was held on Friday for the signing of treaties to incorporate Donetsk, Lugansk, Zaporizhzhia and Kherson into the Russian Federation in the Kremlin, which Kyiv and its international partners condemned as "shams and a violation of international law."

In southern Ukraine, Zelenskyy's hometown Krivyi Rih came under Russian attack by a suicide drone that struck a school early Sunday and destroyed two stories of it, said Valentyn Reznichenko, the governor of Ukraine's Dnipropetrovsk region.

Russia in recent weeks has begun using Iranian-made suicide drones to attack targets in Ukraine. In southern Ukraine, the Ukrainian air force said it shot down five Iranian-made drones overnight, while two others made it through air defenses.

Call for the possible use of low-grade nuclear weapons

Ukraine's recent successes have prompted a close ally of President Vladimir Putin to call for the possible use of low-grade nuclear weapons, according to Reuters. 

"In my personal opinion, more drastic measures should be taken, right up to the declaration of martial law in the border areas and the use of low-yield nuclear weapons," Ramzan Kadyrov, the leader of Russia's southern Chechnya region, wrote on Telegram before Zelenskyy spoke.

Other top officials, including former president Dmitry Medvedev, have suggested that Russia may need to resort to nuclear weapons, but Kadyrov's call was the most urgent and explicit.

Putin said last week that he was not bluffing when he said he was prepared to defend Russia's territorial integrity with all available means, and on Friday made clear this extended to the new regions claimed by Moscow.

Washington says it would respond decisively to any use of nuclear weapons.

Serhii Cherevatyi, spokesperson for Ukraine's eastern forces, said before the capture that Russia had 5,000 to 5,500 troops at Lyman, but the number encircled could be lower. The Russian side did not immediately comment on the report.

Arguments over Moscow's formal recognition of the four regions

Ukraine has adopted sanctions on more than 3,600 Russian individuals and legal entities, according to a statement from Ukraine's economy ministry published on Saturday.

The United States responded to Moscow's formal recognition of the four regions as Russian territory by imposing more sanctions on Russia, targeting hundreds of people and companies, including those in Russia's military-industrial complex and lawmakers.

Russia vetoed a United Nations Security Council resolution introduced by the United States and Albania condemning Moscow's acceptance of the Donetsk, Luhansk, Zaporizhzhia and Kherson regions into Russia following referendums that took place from September 23 through 27.

China on Friday urged all sides to leave space for diplomatic negotiations to resolve the Ukraine crisis.

"China calls on all parties concerned to exercise restraint, refrain from actions that exacerbate tensions and leave space for settlement through diplomatic negotiations," Zhang Jun, China's permanent representative to the United Nations, said in his explanation of China's vote on a Security Council draft resolution on Ukraine.

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(With input from agencies)