Zelenskiy was speaking to Russian journalists in a 90 minute video call, an interview that Russian authorities had pre-emptively warned local media to refrain from reporting.
Zelenskiy spoke in Russian throughout, as he has done in previous speeches when targeting a Russian audience.
Zelenskiy said Russia's invasion had caused the destruction of Russian-speaking cities in Ukraine and said the damage was worse than the Russian wars in Chechnya.
"Security guarantees and neutrality, non-nuclear status of our state. We are ready to go for it. This is the most important point," Zelenskiy said.
Zelenskiy said Ukraine refused to discuss certain other Russian demands, such as the demilitarisation of the country.
Speaking more than a month after Russia invaded Ukraine on February 24, Zelenskiy said no peace deal would be possible without a ceasefire and troop withdrawals.
He ruled out trying to recapture all Russian-held territory by force, saying it would lead to a third world war, and said he wanted to reach a "compromise" over the eastern Donbass region, held by Russian-backed forces since 2014.
Russia says it is conducting a "special military operation" in Ukraine with the aim of demilitarising its neighbour.
Ukraine and its allies call this a pretext for an unprovoked invasion.
Zelenskiy focused on the fate of the eastern port city of Mariupol, under siege for weeks.
Once a city of 400,000 people, it has undergone prolonged Russian bombardment.
"All entries and exits from the city of Mariupol are blocked," Zelenskiy said.
"The port is mined. A humanitarian catastrophe inside the city is unequivocal, because it is impossible to go there with food, medicine and water," he said.
"I don't even know who the Russian army has ever treated like this," he said, adding that, compared to Russian wars in Chechnya, the volume of destruction "cannot be compared".
Zelenskiy pushed back against allegations from Moscow that Ukraine had curbed the rights of Russian speakers, saying it was Russia's invasion that wiped Russian-speaking cities "off the face of the earth".
He also dismissed as "a joke" allegations made by Russia that Ukraine had nuclear or chemical weapons.
Earlier on Sunday, Russia's communications watchdog Roskomnadzor told Russian media to refrain from reporting on the interview done with Zelenskiy and said it had started a probe into the outlets which had interviewed the Ukrainian leader.
"Roskomnadzor warns the Russian media about the necessity of refraining from publishing this interview," it said.
Russian prosecutors said a legal opinion would be made on the statements made in the interview and on the legality of publishing the interview.
A reporter from the Moscow daily Kommersant is among the Russian journalists who had spoken with Zelenskiy via video link.
Journalists from the Meduza and Dozhd media outlets, whose sites are blocked in Russia, were also present.
Meduza published the interview despite the media regulator's warning on Sunday.
The site can still be accessed through alternative internet connections and from abroad.