Ukraine's President Volodymyr Zelensky said Sunday that Lyman, a key town located in one of the four Ukrainian regions that Russia annexed, was "cleared" of Moscow's troops.

The latest development -- a feature of Ukraine's weeks-long counteroffensive against Moscow's invasion -- comes as Russia pushed forward with finalising the annexation of captured Ukrainian territories despite condemnation from Kyiv and the West.

The recapture of Lyman -- which Moscow's forces pummelled for weeks to control this spring -- marks the first Ukrainian military victory in territory that the Kremlin has claimed as its own and has vowed to defend by all possible means.

"As of 12:30 pm (0930 GMT) Lyman is completely cleared. Thank you to our military!" President Zelensky said in a video posted on social media.

Ukraine's army said it had entered Lyman on Saturday, prompting Moscow to announce the "withdrawal" of its troops from the town towards "more favourable lines".

"Now I am optimistic and very motivated. I see the activity on the front line, and how foreign weapons... help us take our lands back," a 33-year-old Ukrainian solider, who uses the nom de guerre "Smoke", told AFP after returning from near Lyman.

In a video address late on Saturday, Volodymyr Zelensky pledged to retake more areas in the country's eastern Donbas region within the week.

Russian court approves annexation

With Russian losses mounting, experts have warned that President Vladimir Putin could turn to nuclear weapons to defend territory -- an option floated by a Putin ally.

Chechen leader Ramzan Kadyrov said Saturday that Russia should consider using "low-yield nuclear weapons" after Moscow's troops were forced out of Lyman.

Putin staged a grand Kremlin ceremony on Friday to celebrate the annexation of the four Ukrainian territories: Donetsk, Kherson, Lugansk and Zaporizhzhia, following referendums denounced as void by Kyiv and its allies.

Despite condemnation from the West, Russia's Constitutional Court on Sunday recognised as lawful the annexation accords signed by Putin with the Moscow-backed leaders of the four Ukrainian territories.

The annexation treaties will be considered by Russia's lower house of parliament, the State Duma, on Monday, according to Duma speaker Vyacheslav Volodin.

The four territories create a crucial land corridor between Russia and the Crimean Peninsula, also annexed by Moscow, in 2014.

Together the five regions make up around 20 percent of Ukraine.

Kyiv has also called for the immediate release of the chief of the Moscow-held Zaporizhzhia nuclear power plant, condemning his "illegal detention" by the Russians.

Ihor Murashov was leaving the plant Friday when he was detained and "driven in an unknown direction" while blindfolded, Ukraine's nuclear agency Energoatom has said.

'Grave concern'

In a statement from the International Atomic Energy Agency (IAEA), its chief Rafael Grossi said Murashov's detention was cause for "grave concern".

Mr Grossi is expected to travel to Kyiv and Moscow "next week", the UN agency added.

Zaporizhzhia -- Europe's largest nuclear energy facility -- has been at the centre of tensions, with Moscow and Kyiv accusing each other of strikes on and near the plant, raising fears of an atomic disaster.

Following the annexations, Washington announced "severe" new sanctions against Russian officials and the defence industry, and said G7 allies support imposing "costs" on any nation backing annexation.

President Zelensky urged the US-led military alliance NATO to grant his country fast-track membership.

He also vowed never to hold talks with Russia as long as Vladimir Putin was in power.

NATO chief Jens Stoltenberg slammed the annexation as "illegal and illegitimate" but remained non-committal after Ukraine said it was applying to join the Western alliance.

Turkey said Saturday Russia's annexation was a "grave violation of the established principles of international law".

Despite Vladimir Putin's warnings prior to the annexation that he could use nuclear weapons to defend the captured territories, Ukraine's Foreign Minister Dmytro Kuleba said Kyiv would "continue liberating our land and our people".