In an interview with the BBC’s John Simpson, Mr Zelensky said the Kremlin has begun to “prepare their society” for the use of nuclear weapons - but said he does not believe Moscow is ready to use them.
Putin declared war on neighbouring Ukraine more than seven months ago but has suffered a string of military setbacks in recent weeks.
Ukraine has been retaking large swathes of territory occupied by Russia, including in regions illegally annexed by the Russian president.
US President Joe Biden on Thursday night warned Mr Putin is “not joking when he talks about the use of tactical nuclear weapons or biological or chemical weapons”, because his military is “significantly underperforming”.
Mr Biden described the risk of nuclear “Armageddon” is at its highest level since the 1962 Cuban missile crisis.
Mr Zelensky, in an interview with the BBC at his presidential office in Kyiv, said in English: “They begin to prepare their society. That’s very dangerous.
“They are not ready to do it, to use it. But they begin to communicate. They don’t know whether they’ll use or not use it. I think it’s dangerous to even speak about it.”
Then, in Ukrainian, he said through a translator: “What we see is that Russia’s people in power like life and thus I think the risk of using nuclear weapons is not that definite as some experts say, because they understand that there is no turning back after using it, not only the history of their country, but themselves as personalities.”
Mr Zelensky denied having urged strikes on Russia by the West, claiming that an earlier remark had been mistranslated.
His comment: “You must use preventive kicks” referred to sanctions, not attacks.
The initial words were denounced by Kremlin spokesman Dmitry Peskov as “an appeal to start yet another world war”. Russian Foreign Minister Sergei Lavrov said it demonstrated why Russia was right to launch its operation in Ukraine.
Mr Zelensky added: “After that translation, they [the Russians] did their way, how it’s useful for them, and began to retranslate it in other directions.”
The Ukrainian president said action was needed now, as Russia’s threats were a “risk for the whole planet”.
Around 500 Russian troops occupy the Zaporizhzhia nuclear power plant, Europe’s largest, which the Kremlin is trying to turn into their property, although Ukrainian staff still operate it.
Mr Zelensky said: “The world can stop urgently the actions of Russian occupiers.
“The world can implement the sanction package in such cases and do everything to make them leave the nuclear power plant.”
US officials have for months warned of the prospect that Russia could use weapons of mass destruction in Ukraine as it has faced strategic setbacks on the battlefield. Mr Biden’s remarks, at a Democratic fundraiser, marked the starkest warnings yet by Washington about the nuclear stakes.
On Friday, US officials said nothing has changed in intelligence assessments in recent weeks to show Putin has imminent plans to deploy nuclear weapons.
One official, who spoke on the condition of anonymity, added that Mr Biden was speaking broadly about the administration’s growing concerns.
Mr Biden was conveying that the White House sees his rhetoric as “reckless and irresponsible” and is taking it seriously, they said.
White House officials this week said they have seen no change to Russia’s nuclear forces that would require a change in the alert posture of the US’s arsenal.
“We have not seen any reason to adjust our own strategic nuclear posture, nor do we have indication that Russia is preparing to imminently use nuclear weapons,” White House press secretary Karine Jean-Pierre said.