Ukrainian troops are reported to have advanced in the east near Bakhmut and in the south near Zaporizhzhia, and have carried out long-range strikes on Russian targets.
The president said on Sarurday: “Counteroffensive and defensive actions are taking place.”
He added that he would not talk in detail about which stage or state the counter-offensive was in.
Russian President Vladimir Putin said in a video interview published Friday that Ukrainian forces had certainly begun their offensive but that attempted advances had failed with heavy casualties.
Speaking in Kyiv, after talks with the Canadian PM Justin Trudeau, Mr Zelensky described the Russian leader’s words as “interesting”.
He also said that Ukraine’s military commanders were in a positive mood, adding: “Tell that to Putin.”
Mr Trudeau is the first foreign leader to visit Ukraine since devastating floods caused by a breach in the Kakhovka dain the Dnieper River. He offered financial , military and moral support for Ukraine.
Thousands of people are believed to be trapped after the dam’s collapse .
Mr Trudeau has already provided £4.7bn in aid since the began in February 2022. The country has also announced £6m for humanitarian assistance for the flood response.
Mr Trudeau said the dam’s collapse was “a direct consequence of Russia’s war”.