Putin's remarks on Friday came a week after Ukraine, along with Russia and separatists in eastern Ukraine, signed an accord to pull back heavy weaponry and to hold an election in the area at a later date.
The pullback has not occurred because of shelling from both sides and threats from Ukrainian hardliners to hamper the disengagement, prompting Zelenskiy to argue that there won't be one so long as there are those who "don't want the disengagement" and "do random shooting."
Russia has said the pullback needs to take place before a summit scheduled for this month between Putin, Zelenskiy, French President Emmanuel Macron and German Chancellor Angela Merkel. Russia has vehemently denied its role in funding, arming and training the rebels, insisting that Kyiv faces a civil war.
Several opposition parties and far-right groups have opposed Zelenskiy's commitment to pull back weaponry in two locations near the separatist-held areas as well as his promise to support a local election, saying he's giving away too much.
Putin said that Russia is supportive of the initiatives to bring peace to the separatist-held eastern Ukraine where 13,000 people have died since 2014 but said it is up to Zelenskiy and the Ukrainian establishment to see through the accords.
"We've agreed on the pullback of the forces but the current president still can't ensure the pullback," Putin said at a meeting in Turkmenistan. "He just can't."
Zelenskiy scored a major political victory last month when he successfully negotiated with Putin a major prisoner exchange, which saw 70 people — some of whom were imprisoned for several years — return home in Ukraine and Russia, respectively.
Zelenskiy, who was a successful comedian and entertainment producer before he won the election by a landslide in April, made it his top priority to bring an end to the war in Ukraine's industrial heartland.
Far-right groups are planning to stage a major rally in the capital Kyiv on Monday against Zelenskiy's peace plan.
Speaking at a military awards ceremony in Odessa on Friday, Zelenskiy said he works "24 hours a day" to bring about peace but insisted that he stands firm on Ukraine's commitment to hold a local election in eastern Ukraine as long as the vote is held under the Ukrainian law and in the presence of international observers.
Kyiv's Joint Forces' Operation in the east said Friday that their positions have come under repeated shelling in the past 24 hours.
In Donetsk, separatist commander Ruslan Yakubov told the DAN News website that the rebel forces were ready for the pullback but did not go ahead because Kyiv did not indicate its readiness.
END/AP/UNB/SN