Putin's comments came after the United States last week said it would supply Ukraine with advanced missile systems, the latest in a long list of weaponry sent or pledged for the pro-Western country.
Ukraine has asked for ever more potent arms and its deputy defence minister stressed Sunday this support was needed until Russia was defeated.
"We have already entered into a protracted war and we will need constant support," Ganna Malyar told local media.
"The West must understand that its help cannot be a one-time thing, but something that continues until our victory," she added.
'They are bombing everything'
Ukrainian officials earlier Sunday said Russian missiles hit railway infrastructure sites in the first such strikes on Kyiv since 28 April.
Russia said the strikes had destroyed tanks supplied to Ukraine by eastern European countries.
"High-precision, long-range missiles fired by the Russian Aerospace Forces on the outskirts of Kyiv destroyed T-72 tanks supplied by eastern European countries and other armoured vehicles that were in hangars," Russian defence ministry spokesman Igor Konashenkov said.
One person was wounded, and AFP reporters saw several buildings with blown-out windows near one of the sites that was targeted.
Leonid, a 63-year-old resident who used to work at the facility, said he heard three or four explosions.
"There is nothing military there but they are bombing everything," he said.
Vasyl, 43, said he heard five blasts.
"People are afraid now," he said, walking back to his damaged home with two loaves of bread.
'It's a horror show'
In the east of the country, Russian and Ukrainian forces fought for control of Severodonetsk -- the largest city still in Ukrainian hands in the Lugansk region of the Donbas region.
Russian forces have been making slow but steady advances in the region in recent weeks after being beaten back of retreating from other parts of the country, including Kyiv.
"The Russians were in control of about 70 per cent of the city, but have been forced back over the past two days," Gaiday said on Telegram.
"They are afraid to move freely around the city."
Russia's army had claimed Saturday some Ukrainian military units were withdrawing from Severodonetsk, but mayor Oleksandr Striuk said Ukrainian forces were fighting to retake the city.
"We are currently doing everything necessary to re-establish total control" of the city, he said in an interview broadcast on Telegram.
In the neighbouring city of Lysychansk, pensioner Oleksandr Lyakhovets said he had just enough time to save his cat before the flames engulfed his flat after it was hit by a Russian missile.
"They shoot here endlessly... It's a horror show," the 67-year-old told AFP.
On Sunday, the press service of the Ukrainian president's office reported nine civilians killed in the Donetsk and Lugansk regions from shelling.
Western powers have imposed increasingly stringent sanctions on Russia but divisions have emerged on how to act, particularly on whether to engage in dialogue with Russia or not.
French president Emmanuel Macron said Friday Putin had committed a "fundamental error" but that Russia should not be "humiliated" to allow for a diplomatic solution.
Ukrainian foreign minister Dmytro Kuleba reacted Saturday by saying such calls "only humiliate France" and any country taking a similar position.
Speaking from the apostolic palace in St Peter's Square Sunday, Pope Francis renewed calls for "real negotiations" to end what he called the "increasingly dangerous escalation" of the war.
Apart from the human toll, the conflict has caused widespread damage to Ukraine's cultural heritage.
On Saturday, Ukrainian officials reported a large Orthodox wooden monastery, a popular pilgrim site, had burnt down and blamed Russia shelling.
Russian troops now occupy a fifth of Ukraine's territory, according to Kyiv, and Moscow has imposed a blockade on its Black Sea ports, sparking fears of a global food crisis. Ukraine and Russia are among the top wheat exporters in the world.
The United Nations said it was leading intense negotiations with Russia to allow Ukraine's grain harvest to leave the country.
Away from the battlefield, Wales dashed Ukraine's dreams of reaching its first football World Cup since 2006 with a 1-0 victory.
Before the game in Cardiff City Stadium Sunday, the Ukrainian national anthem was applauded by all sides.