Russia-Ukraine updates: Putin suspends key US-Russia nuclear treaty in speech denouncing West

Ukrainian President Volodymyr Zelenskyy on Monday vowed to reclaim all territory lost to Russian forces.

"Ukraine is returning its own. And it will return the Kharkiv region, Luhansk region, Donetsk region, Zaporizhzhia region, Kherson region, Crimea. Definitely our entire water area of the Black Sea and the Sea of Azov, from Zmiinyi Island to the Kerch Strait," he said in his daily address. "This will happen. This is ours. And just as our society understands it, I want the occupiers to understand it, too. There will be no place for them on Ukrainian land."

Zelenskyy said his message to Russian fighters is that if they want to survive, it's time for them to flee or surrender.

"The occupiers should know, we will oust them to the border -- to our border, the line of which has not changed. The invaders know it well," he said. "If they want to survive, it is time for the Russian military to flee. Go home. If you are afraid to return to your home in Russia, well, let such occupiers surrender, and we will guarantee them compliance with all norms of the Geneva Conventions."

White House spokesman John Kirby said Monday that Russia should agree to a demilitarized zone around the Zaporizhzhia nuclear power plant and that a controlled shutdown of the reactors "would be the safest and least risky option in the near-term."

Kirby also expressed support for the IAEA mission to the power plant.

"We fully support the International Atomic Energy Agency Director General Grossi’s expert mission to the power plant, and we are glad that the team is on its way to ascertain the safety, security and safeguards of the systems there, as well as to evaluate the staff’s working conditions," he said. "Russia should ensure safe, unfettered access for these independent inspectors."

-ABC News’ Ben Gittleson

Ukrainian forces have launched a major counteroffensive in multiple directions in the southern part of Ukraine, Natalia Humeniuk, a spokesperson for Ukraine's Operational Command, said Monday.

Humeniuk said the situation in the south remains "tense," but controlled.

Ukrainians have been targeting strategic Russian command posts and slowly advancing toward Kherson for weeks. Kherson was first major city in the south to be captured by Russian forces following the invasion.

Russian military issued a statement confirming the offensive and claiming Ukraine sustained heavy losses.

Meanwhile, at least 12 missiles have struck Mykolaiv, which remains under Ukraine's control in the south. Two people were killed and 24 were wounded, according to the governor of Mykolaiv Oblast.

-ABC News' Max Uzol and Natalia Shumskaia

Oleksiy Kovalyov, a Ukrainian official who was accused of treason for openly collaborating with Russia, was shot and killed in his home on Sunday in Hola Prystan, Kherson Oblast, according to preliminary information from the Investigative Committee of Russia (SKR). An unidentified woman was also killed, SKR said.

Kovalyov was a Ukrainian lawmaker from President Volodymyr Zelenskyy's party who was accused of treason; criminal proceedings were initiated by Ukraine's State Bureau of Investigations in June. He is one of the highest-ranking Ukrainian defectors who fled to Kherson after the invasion and openly collaborated with Russia. He was appointed by the Russians as the deputy head of the Kherson Military-Civil Administration.