Zelenskiy was speaking to Germany's BILD TV in an interview published hours after the Russian president announced a partial mobilisation and warned that Russia would respond to what he called US-led "nuclear blackmail".
It was Russia's first such mobilisation since World War II and signified the biggest escalation of the Ukraine war since the Russian invasion in February.
"I don't believe that he (Putin) will use these weapons. I don't think the world will allow him to use these weapons," Zelenskiy said, according to a text published by the newspaper.
"Tomorrow Putin can say: apart from Ukraine, we also want a part of Poland, otherwise we will use nuclear weapons. We cannot make these compromises."
Putin made the announcement in a televised address in which he also announced moves to annex swaths of Ukrainian territory and threatened to use nuclear weapons to defend Russia, declaring: "It's not a bluff".
Flights out of Russia quickly sold out and jailed opposition leader Alexei Navalny called for mass demonstrations against the mobilisation.
Russians said some people were already receiving call-up notices, and police were barring men from leaving one city in the south.
Independent protest monitoring group OVD-Info said more than 1300 people had been detained in protests by Wednesday evening.
In a country that counts millions of former conscripts as reservists, Putin's "partial mobilisation" decree gave no clue as to who would be called up.
Defence Secretary Sergei Shoigu said 300,000 people would be mobilised from a pool of 25 million.
Contracts of professional troops would be extended indefinitely.
Putin also effectively announced plans to annex four Ukrainian provinces, saying his government would assist with referendums on joining Ukraine's Luhansk, Donetsk, Zaporizhzhia and Kherson regions to Russia, and implement the results.
Ukraine has recaptured swathes of its territory after a lightning counter-offensive in recent weeks, inflicting mounting casualties on Russian troops.
Putin's mobilisation has come in response to Russia's failings on the battlefield, Zelenskiy said.
"He sees that his units are simply running away," Zelenskiy said, adding that Putin "wants to drown Ukraine in blood, including the blood of his own soldiers".
Zelenskiy also brushed off plans by four Russian-occupied regions of Ukraine to hold referendums on September 23-27 on joining Russia, saying they were a "sham" that would not be recognised by most countries.
"We will act according to our plans step by step. I'm sure we will liberate our territory," he said.
European Union foreign ministers, in New York for the United Nations General Assembly, called an emergency meeting for late on Wednesday to discuss new sanctions and weapon deliveries for Ukraine after Putin's order.
"It's clear Russia wants to destroy Ukraine," EU foreign policy chief Josep Borrell said.
"We will not be intimidated."
Calling a mobilisation is possibly the riskiest domestic political move of Putin's two decades in power, and follows months of Kremlin promises it would do no such thing.
The war has so far appeared to enjoy popular support in a country where independent media have all been shut down and all public criticism of the "special military operation" is banned.
But for many ordinary Russians, especially in the urban middle classes, the prospect of being sent to fight would be the first hint of the war affecting them personally.
"It is clear that the criminal war is getting worse, deepening, and Putin is trying to involve as many people as possible in this," jailed opposition leader Navalny said in a video message recorded and published by his lawyers.
"He wants to smear hundreds of thousands of people in this blood."
Moments after Putin's announcement, recruitment offices had already handed packs of conscription papers to homeowners' associations, said St Petersburg human rights lawyer Pavel Chikov, who advises clients on conscription.
Medics in Moscow were "receiving summonses from recruitment offices en masse to come and receive mobilisation orders," he said on Telegram.
