In a battlefield rebuttal to President Vladimir Putin’s annexation a day earlier, Ukrainians surrounded several thousand Russian troops near the key town in one of four Moscow-held territories.
Lyman, located in the "annexed" Donetsk region, is a town Moscow's forces pummelled for weeks to capture this spring.
Now, Ukraine's army said it had "encircled" a Russian grouping near the town, estimating it to be around 5,000 troops.
The Kremlin-backed leader of Donetsk said Friday that Russian troops and their allies were holding on to Lyman with "their last strength".
The capture of the town would be a major setback for Russia after Vladimir Putin proclaimed the annexation of the Donetsk region, along with three other regions, at a ceremony in Moscow on Friday condemned by Kyiv and the West as a farce.
The four annexed territories create a crucial land corridor between Russia and the Crimean Peninsula, annexed by Moscow in 2014.
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Sources: Reuters, AFP