KYIV, Ukraine — In a display of pageantry intended to give Moscow’s land grab a veneer of legitimacy, Russian proxy officials in occupied areas of Ukraine appealed to President Vladimir Putin of Russia on Wednesday to annex the regions.

The annexation requests had an air of order and formality at odds with the chaos Russia’s leaders are facing both on the battlefield, where they continue to suffer losses, and at home, where tens of thousands of Russians are fleeing the country to avoid a military draft.

The requests from the Russian proxies followed sham referendums that ended Tuesday in four regions in Ukraine and that, to no one’s surprise, purported to put voters’ stamp of approval on joining Russia. Many of the ballots were cast at the point of a gun, witnesses said.

The annexation push occurred as the European Union moved to impose new sanctions aimed at punishing Russia over its latest actions. The draft measures include an oil price cap, trade restrictions and blacklisting several individuals responsible for the referendums.

On Feb. 24, Russian forces rolled across the border and began laying waste to Ukrainian cities. But when it comes to annexation, Russian officials appear to want at least a patina of legality — even as most of the world condemns the referendums as patently unlawful.

Under Russia’s 1993 constitution, Moscow cannot annex areas of a neighboring country without consent. And so the moves taking place are meant to check boxes under Russian law governing how to claim land in a neighboring country.

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As a practical matter, much of the territory Russia is moving to claim is not under its control, and the Ukrainian military is whittling away even more.

More about Russia’s war on Ukraine

On Wednesday, Ukraine continued to reclaim more towns and villages in the east while pounding Russian positions in the south. Destroyed Russian tanks and the bodies of Russian soldiers littered the roadside outside the village of Oskil as Ukrainian soldiers pushed toward the strategically important city of Lyman.

The destruction illustrated the challenges thinly spread and badly battered Russian forces are facing as they try to defend against multiple Ukrainian offensives. Russia’s heavy losses led Putin to take the politically risky step of ordering the nation’s first mass mobilization since World War II.

But at least 200,000 Russians have left the country since Putin announced the partial military mobilization, according to figures provided by Russia’s neighbors.