Ukraine's President Volodymyr Zelenskyy has acknowledged that Ukrainian troops are engaged in a fierce battle with Russian forces trying to take back territory in the Kursk region in western Russia.

Zelenskyy posted a comment on social media on Monday on Ukraine's cross-border offensive that began in August.

He wrote that Russia has been trying to break through Ukraine's defense in the Kursk region for five days. Zelenskyy added, "The guys are holding on and counterattacking."

Ukraine's top prosecutor said on Sunday that Russian forces are suspected of shooting and killing nine Ukrainian prisoners of war in the Kursk region. Prosecutor General Andriy Kostin said his office has opened a criminal investigation into the alleged execution.

The US-based Institute for the Study of War says it has recently observed an increase in Russian forces executing Ukrainian prisoners of war. It says, "Russian commanders are likely writ large condoning, encouraging, or directly ordering" the executions.

Meanwhile, Russia's defense ministry said on Monday that troops have seized a settlement in the southern region of Zaporizhzhia. Russian forces are apparently stepping up their offensive in areas outside their main front in the eastern Donetsk region.