Zelenskyy said Sunday that Ukraine retook some territory from Russia in the Kherson region.
Ukraine's counteroffensive means Russia does not occupy all of the four regions it wants to annex.
Russia did not completely take over some of the regions, and Ukraine has retaken land in all of them.
Ukraine said it has taken back more territory in the east of the country from Russian troops, leaving Moscow with even less control over the four regions that it is trying to annex.
President Vladimir Putin on Friday said his forces were annexing four regions — Kherson, Zaporizhzhia, Donetsk, and Luhansk — and making them part of Russia. In reality, however, Russia does not fully occupy any of the regions.
Ukraine had already retaken some of those regions, and it was fighting against and taking back territory from Russian troops even as Putin made his celebratory speech.
Ukraine claimed total control of Lyman, a key strategic city in Donetsk, on Sunday.
Ukrainian President Volodymyr Zelenskyy then said later in the day that his troops had made more gains: "But the successes of our soldiers are not limited to Lyman."
Zelenskyy said Ukraine had "liberated" the towns of Arkhanhelske and Myroliubivka in Kherson.
While that village is small and near the border, it means Ukraine has a symbolic victory: Russia does not control 100% of the territory of any of the regions it says it is making part of Russia.
It is not clear if Russia intends to consider every part of each of the regions to be part of Russia.
Kremlin spokesperson Dmitry Peskov said on Monday that Russia would "consult" with residents as to where to put the borders, Al Jazeera reported.
"We will continue to consult with people who live in these areas," he said.
Kremlin spokesperson Dmitry Peskov said on Friday that attacks on the areas that Putin annexes would be considered an attack on Russia, The Guardian reported — which means Putin's move could result in a rapid ramping up of the war.
Ukraine and the West, including the EU, NATO, and the US, said they will not recognize Putin's annexations.
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