Command spokesperson Natalia Humeniuk confirmed the offensive in a news briefing and said it included the Kherson region.
Ukraine has regularly stated its intention to retake its south, and in particular the city of Kherson, the only regional capital that Russia has been able to capture from Ukraine since it invaded six months ago.
The region lies north of the Russian-held Crimean peninsula and has coasts on the Black Sea and the Sea of Azov.
Humeniuk said at the briefing that recent strikes on Russia’s southern logistical routes had “unquestionably weakened the enemy”. More than 10 Russian ammunition dumps had been hit over the last weeks.
However, she declined to be drawn into giving more details about the new offensive.
Russia’s forces in the south are “rather powerful” and have been built up over a long time, she told the briefing.
“The counter-offensive is already ongoing for a while (in the sense of) exhausting the enemy and not giving him an opportunity to advance,” Humeniuk told public broadcaster Suspilne, adding that the offensive phase of this had begun on Monday.
Shortly after the announcement, Ukraine’s presidential chief of staff, Andriy Yermak, wrote a cryptic message on Telegram proclaiming “our Kherson is ahead.”