President Volodymyr Zelensky, always adept at messaging, used his latest Independence Day speech on Saturday to drive home the idea that Ukraine is taking the fight to Russia, even as his troops struggle along the front line in the east.

He said the video of the speech was filmed near the site where his troops began a cross-border offensive into Russian territory nearly three weeks ago that caught Moscow by surprise and yielded a bounty in Russian prisoners of war. That paid immediate dividends on Saturday when the two sides each sent 115 prisoners to the other in an exchange brokered by the United Arab Emirates.

Mr. Zelensky’s video was prerecorded from what he described as a location along the Psel River, an area frequently targeted by Russian artillery.

“Whoever wished misery upon our land shall find it in their own home,” Mr. Zelensky said of the incursion, which has pushed into the Kursk region of southwestern Russia.

He called his military’s operation — which has come after two and a half years of Russia’s brutal, all-out invasion of Ukraine — a “boomerang for evil.”

In the prisoner exchange, Ukraine said it had freed soldiers held in Russia since early in the invasion. That included dozens of soldiers who had held out for months in the siege of the Azovstal steel mill in Mariupol, before surrendering on the orders of Mr. Zelensky when escape or further resistance became hopeless.