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.
Image: A member of Ukraine’s 25th Separate Airborne Brigade keeps an eye on the sky as he rides in a car near the front line. Pic: Reuters
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.
Image: A Ukrainian soldier launches a drone into the air, near Pokrovsk. Pic: Reuters
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.
Donald Trump disparaged the Russian military and backed Ukraine to retake all its occupied territory in an astonishing about-turn on the war.
In a post on Truth Social, made after talks with Volodymyr Zelenskyy at the United Nations in New York, the US president said a return to “the original borders from where this war started is very much an option”.
“I think Ukraine, with the support of the European Union, is in a position to fight and WIN all of Ukraine back in its original form,” he wrote.
Mr Trump said “time, patience, and the financial support of Europe and, in particular, NATO” could help Kyv win back lost territory, and said Russia was in “economic trouble”.
He said Moscow had been “fighting aimlessly” for three-and-a-half years – and had it been a “real military power” it would have defeated Ukraine in less than a week.
“This is not distinguishing Russia. In fact, it is very much making them look like ‘a paper tiger’,” he added.
He later admitted he was surprised by Mr Trump’s comments, telling Fox News’ Special Report he has a better relationship with the president than before.
Image: Donald Trump and Volodymyr Zelenskyy at the United Nations. Pic: Reuters
Trump’s patience not ‘infinite’
Mr Trump also appeared to pour cold water on his hopes of persuading Vladimir Putin to sign a peace deal.
Speaking to Emmanuel Macron at the UN summit, he said their relationship had turned out to be meaningless.
Just last month, Mr Trump rolled out the red carpet for the Russian president at a summit in Alaska – in a push to expedite the war’s conclusion.
Before returning to the White House, he repeatedly claimed he’d be able to end the conflict in 24 hours.
Speaking at the UN Security Council, his secretary of state, Marco Rubio, admitted ending the war had proven an “extraordinary challenge”.
He said Mr Trump had “worked on it tirelessly”, but warned Russia his patience is not “infinite”.
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4:11
Rigby to Trump: Was Putin’s Alaska invite a mistake?
The US president has previously suggested Ukraine will never be able to reclaim all the territory Russia has occupied since seizing the Crimean Peninsula in 2014.
Ukraine has lost large areas of land in the east of the country.
In the Donetsk region, Russia now controls about 70% of the territory. Kyiv’s forces have been pushed back to four cities analysts have dubbed the “fortress belt”.
Moscow has partly annexed three other regions, too: Luhansk in the east, Zaporizhzhia and Kherson further west.
Image: The situation in Ukraine on 19 September
Trump tells NATO to shoot down Russian jets in its skies
Meanwhile, Russia appears to be provoking its neighbours to the west. Last week, Estonia said three Russian MiG-31 fighter jets violated its airspace for 12 minutes before Italian NATO jets escorted them away.
While talking to Mr Zelenskyy at the UN, Mr Trump was asked by reporters whether he thought NATO should shoot down any Russian planes that entered NATO airspace.
“Yes, I do,” Mr Trump replied.
On Truth Social, he said the US would continue to supply weapons to NATO, and it was for the alliance to “do what they want with them”.
Mr Trump also suggested the Russian people are not aware of “what is really going on with this war”.
He added: “Most of their money is being spent on fighting Ukraine. Putin and Russia are in big economic trouble and this is the time for Ukraine to act.”
He has called on European and NATO allies to increase economic sanctions on Moscow.
In a joint statement following the president’s comments, G7 foreign ministers said discussions were ongoing about additional economic sanctions on Russia.
So, why the handbrake turn from framing negotiations as the most practical outcome to a new-found confidence in Ukraine, when supported by its European neighbours and NATO?
Image: Trump held talks with Zelenskyy at the UN. Pic: Reuters
Firstly, it could be the military and economic reality on the ground. Russia’s paying a high price for the war, both in manpower and finances.
Trump has acknowledged that Moscow is in “big economic trouble”, which strengthens the case for Ukraine prevailing with Western help.
Ukraine’s resilience has also shifted perceptions – the impossible now looking possible if allies remain committed.
Secondly, it could be the influence of allies. European leaders flew to Washington en masse last month to urge caution in dealings with Putin.
European NATO members have stepped up aid to Ukraine, further weakening the President’s rhetoric about America carrying the financial burden.
He’s suddenly aligning himself with European countries, endorsing the shooting down of Russian planes violating their airspace.
Thirdly, it could be more about domestic politics, with the president under bipartisan scrutiny at home over his “softly, softly” approach to Russia.
A tougher national defence posture could help him consolidate support among Republicans, while also appealing to moderates, who regard the defence of Ukraine as a test of national credibility.
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0:16
Zelenskyy on Trump’s ‘big shift’ over Ukraine
Trump versus the world
There’s another factor worth considering – Trump’s negotiating tactic. He has a long record of changing position to gain leverage.
Talk of compromise might have been the strategy for getting Ukraine and Russia into talks, but with Russia showing no willingness to compromise, his calculation shifting back to the restoration of Ukraine.
Whatever the reason for his change of heart, and whether it translates into US policy, the last three days have shown an emboldened Trump.
From his declaration of “hate” for his opponents during a memorial service for Charlie Kirk, to his sensational claim to have “found an answer on autism”, to his derision of the UN, he’s unfiltered right now.
Place him in front of a microphone or online, and it’s Trump versus the world.
Acclaimed Italian actress Claudia Cardinale, who starred in The Pink Panther and Once Upon A Time In The West, has died aged 87, according to French media reports.
The actress, who starred in more than 100 films and made-for-TV productions, died in Nemours, France, surrounded by her children, her agent told the AFP news agency.
At the age of 17 she won a beauty contest in Tunisia, where she was born to Sicilian parents, and was rewarded with a trip to the Venice Film Festival, kick-starting her acting career.
She had expected to become a schoolteacher before she entered the beauty contest.
Image: Claudia Cardinale at the Prix Lumieres awards ceremony in Paris in January 2013. Pic: AP
Cardinale gained international fame in 1963 when she starred in both Federico Fellini’s 8-1/2 and The Leopard.
She went on to star in the comedy The Pink Panther and Sergio Leone’s Once Upon A Time In The West in 1968.
She considered 1966’s The Professionals as the best of her Hollywood films.
When she was awarded a lifetime achievement at the Berlin Film Festival in 2002, she said acting had been a great career.
“I’ve lived more than 150 lives, prostitute, saint, romantic, every kind of woman, and that is marvellous to have this opportunity to change yourself,” she said.
“I’ve worked with the most important directors. They gave me everything.”
Cardinale was named a goodwill ambassador for the UN Educational, Scientific and Cultural Organisation for the defence of women’s rights in 2000.