The US president's direct appeal to Putin came after Ukrainian President Volodymyr Zelensky urged his allies to put Russia under more pressure to halt its invasion.
Zelensky cut short a trip to South Africa to deal with the aftermath of the strikes, the latest in a wave of Russian aerial attacks that have killed dozens of civilians.
"I am not happy with the Russian strikes," Trump said on social media. "Not necessary, and very bad timing. Vladimir, STOP!"
Trump, who is accused of favoring Russia and has often vilified Zelensky, was asked by reporters what concessions Moscow had offered in negotiations to end the war.
"Stopping taking the whole country -- pretty big concession," he replied.
Russia invaded Ukraine in 2022, hoping to take the country in days, but has since been bogged down in a bloody war with huge casualties on both sides.
Trump on Wednesday accused Zelensky of frustrating peace efforts by ruling out recognizing Russia's claim over Crimea, a territory the US president said was "lost years ago."
In contrast, NATO Secretary-General Mark Rutte said Thursday it was Russia, not Ukraine, that needed to move forward in negotiations.
"The balls are clearly in the Russian court now," Rutte told reporters at the White House after meeting Trump.
- Ceasefire deal -
Trump's envoy Steve Witkoff is due in Russia this week where he is expected to hold another round of ceasefire talks with Putin.
Ukraine has been battered by aerial attacks throughout Russia's three-year invasion but strikes on Kyiv, better protected by air defenses than other cities, are less common.
Zelensky said Russia used a North Korean ballistic missile in the strikes, which killed at least 12.
The assault threw more doubt on US efforts to push Russia and Ukraine to agree to a ceasefire, after Trump lashed out at Zelensky this week for not being willing to accept Russian occupation of Crimea, annexed by Moscow in 2014.
"We do everything that our partners have proposed, only what contradicts our legislation and the Constitution we cannot do," Zelensky said in response to a question about Crimea.
Zelensky also questioned whether Kyiv's allies were themselves doing enough to force Putin to agree to a full and unconditional ceasefire.
"I don't see any strong pressure on Russia or any new sanctions packages against Russia's aggression," Zelensky said, highlighting that Trump had previously warned of repercussions if Moscow did not agree to pause the fighting.
- 'Pulled out of the rubble' -
Loud blasts sounded over the Ukrainian capital around 1:00 am (2200 GMT) after air raid sirens rang out across Kyiv, AFP journalists said.
Russia fired at least 70 missiles and 145 drones at Ukraine between late Wednesday and early Thursday, the main target being Kyiv, the Ukrainian air force said.
"As of 5:30 pm, the death toll in Kyiv's Sviatoshinsky district has risen to 12," Ukraine's state emergency services reported, with the number of wounded rising to 90.
Russia said it had targeted Ukraine's defense industry, including plants that produced "rocket fuel and gunpowder."
Olena Davydiuk, a 33-year-old lawyer in Kyiv, told AFP she saw windows breaking and doors "falling out of their hinges."
"People were being pulled out of the rubble," she added.
In Sviatoshinsky, west of Kyiv, an AFP journalist saw a body bag containing one of the victims set on a strip of grass.
A woman sat on a small folding chair stroking the arm of another victim, the body covered in a striped blue sheet.
Moscow has launched some of its deadliest aerial strikes over the last month -- defying Trump's push to bring about a rapid end to the bloodshed.
A ballistic missile strike on the center of northeastern city of Sumy killed at least 35 on April 13.
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