Russia fired more than 90 missiles and around 100 drones during the barrage, according to Kyiv, with Ukrainian President Volodymyr Zelensky urging his allies to respond firmly to what he dubbed Russian "blackmail".
Putin said the fresh bombardment was a "response" to Ukrainian strikes on his territory with Western missiles.
The nearly three-year war has seen a sharp escalation in recent days, with both sides deploying new weapons in a bid to gain the upper hand before US president-elect Donald Trump takes office in January.
"We do not rule out the use of Oreshnik against the military, military-industrial or decision-making centres, including in Kyiv," Putin told a press conference in the Kazakh capital Astana, referring to the hypersonic missile.
Kyiv's government district -- an area of the capital where multiple government buildings are located -- is protected with intense security, but fears for it have risen over the last week.
Russia tested its new Oreshnik ballistic missile on Ukraine last week, and Putin boasted on Thursday that firing several of the weapons at once would have the equivalent force of a nuclear strike, or a "meteorite" hit.
The Kremlin chief said the overnight barrage was a "response to continued attacks on our territory by (US) ATACMS missiles".
"As I have said repeatedly, there will always be a response from our side."
- 'Despicable escalation' -
The strikes came as Ukrainians braced for a tough winter, with much of the country's energy infrastructure already damaged by almost three years of war, and as Russian troops advanced in eastern Ukraine.
Putin suggested he had hopes for Trump's second term, describing the Republican on Thursday as an "intelligent person", capable of finding a "solution", without specifying what he was referring to.
The Russian leader spoke hours after the overnight barrage that left more than half a million in Ukraine's western Lviv region cut off from electricity.
Another 280,000 in the western Rivne region and 215,000 in the northwestern Volyn region also lost power, officials said.
Ukraine's emergency services said the Russian overnight strikes inflicted damage in 14 regions across the country, with the nation's west hard-hit.
Zelensky said that Russia had also fired "cluster munitions" during the attack, calling it a "very despicable escalation of Russian terrorist tactics".
US President Joe Biden on Thursday said the attack showed the "urgency" of backing Kyiv ahead of Trump's return to office in January.
"This attack is outrageous and serves as yet another reminder of the urgency and importance of supporting the Ukrainian people in their defense against Russian aggression," Biden said in a statement.
AFP journalists in the capital heard blasts ring out overnight as air defence systems targeted Russian drones and missiles, with locals crowding into the underground metro system for cover.
The energy ministry said it was the eleventh massive Russian attack on Ukraine's civilian energy infrastructure this year.
A senior UN official, Rosemary DiCarlo, this month warned that Russia's attacks on Ukraine's energy infrastructure could make this winter the "harshest since the start of the war".
- Putin boasts of new missile -
Since Moscow shocked the West and Kyiv by testing its new ballistic missile on the city of Dnipro last week, Russian officials have touted the weapon's might.
In Astana, Putin said the Oreshnik could turn anything "into dust" and hit at a temperature comparable to "the surface of the sun".
He said Russia was "forced" to "test (the weapon) in combat conditions" after Kyiv's first strike on Russian territory using ATACMS.
Putin said Thursday the Oreshnik could travel "around three kilometres per second".
Putin also claimed Russia knew how many long-range weapons were given to Kyiv and where they were located.
Polish Prime Minister Donald Tusk said Putin's threat to strike Kyiv was a "testament to weakness", adding that the West would not be deterred by his words.
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