Kyiv claims to now control almost 500 square miles (around 1,300 square km) and it has taken hundreds of prisoners of war.
“We don’t need their land. We don’t want to bring our Ukrainian way of life there,” Mr Zelenskyy told NBC News during his first one-on-one interview since the offensive.
Instead, Ukraine will reportedly “hold” the territory as a key part of Mr Zelenskyy’s “victory plan” to end the war.
“For now, we need it,” he said of Kursk, adding he will present the proposal to hasten the war’s end to international partners like the US – where he is due to visit later this month.
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During the interview, Mr Zelenskyy refused to rule out seizing more territory and since the Kursk incursion, Ukraine has had at least one cross-border attack repelled by Russia.
The August offensive was kept a secret from everyone, including allies and reportedly Ukraine’s own intelligence service.
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This, Mr Zelenskyy said, was due to lessons learned from the previous summer’s counter-attack which was widely reported on – giving Russia time to prepare, he claimed.
Russia’s eastern advance in face of Kursk incursion
The Kursk incursion changed the face of the war, opening up a second major front in which Ukraine hopes to benefit.
But it isn’t apparent how much it has impacted Russia’s ability to operate, or if it has drawn forces from elsewhere.
In the east of the country, Russia has been slowly advancing towards strategically important Ukrainian settlements.
Losing the likes of Pokrovsk and the neighbouring Toretsk, in the Donetsk region, would be a blow to Ukraine, experts have said.
However, Moscow has so far been unable to dislodge Kyiv’s forces from Kursk and the episode represents a major embarrassment for Vladimir Putin.
Poltava ballistic attack
Elsewhere in the ongoing war, on Tuesday, at least 51 people were killed and more than 200 injured in a Russian ballistic missile attack on the city of Poltava.
The missiles struck a military academy and nearby hospital, officials said.
Three days of mourning have been declared to mark one of the single deadliest attacks of the war.
Rescue efforts in the city were ongoing into the evening, with Mr Zelenskyy saying, as of 9pm UK time, that people were still trapped under the rubble.
“I am grateful to all the rescuers, doctors, medical nurses, and all the Poltava residents who have joined in to help, donated blood, and who provide support,” he said.
“We know that there are people under the rubble of the destroyed building. Everything is being done to save as many lives as possible.”
Elsewhere, Mr Zelenskyy conducted a shakeup of the Ukrainian government, ahead of his visit to the US.
“Autumn will be extremely important. Our state institutions must be structured in such a way so that Ukraine can achieve all the results it needs,” he said.
“For this, we must strengthen some areas of the government and changes in its makeup have been prepared. There will also be changes in the (president’s) office.”
Early on Wednesday, Russia launched a drone attack on Kyiv, according to Ukraine’s military.