Ukraine struck the small town of Rylsk in Russia's Kursk region, killing five and wounding 12, said the governor, Alexander Khinshtein.
An earlier toll from the governor said six people were killed.
Khinshtein accused Kyiv of firing US-supplied HIMARS rocket systems on civilian targets, saying the strike damaged buildings including a school and the dormitory of a pilot training college.
Videos on social media showed cars on fire, debris strewn on roads and buildings with windows blown out.
The border region is partly occupied by Ukrainian forces
Russian foreign ministry spokeswoman Maria Zakharova told TASS state news agency Moscow would raise the attack at a UN Security Council meeting Friday.
Russia last year accused Ukraine of using cluster munitions to attack the town of around 15,000 residents located around 20 miles (30 km) from the border.
The attack came hours after Russian missiles hit central Kyiv early Friday, killing at least one person and damaging embassies.
Moscow claimed the dawn attack as retaliation for a strike using Western missiles on a chemical plant earlier in the week.
Ukraine's air force said Russia launched five Iskander missiles on Kyiv, all of which it managed to shoot down, but falling debris damaged several districts.
- 'Explosions after explosions' -
Russian aerial attacks regularly target the capital but rarely cause significant damage as Kyiv is well protected by air defence, nearly three years into Russia's invasion.
"There were explosions after explosions in a row," said 45-year-old Ksenia, who was staying at a hotel near the site of the wreckage.
The strikes killed a 53-year-old man and wounded 13 people, most suffering from shrapnel injuries, city officials said.
They also damaged a building housing the embassies of Argentina, Palestine, North Macedonia, Portugal and Montenegro, and Albania's diplomatic mission, the Ukrainian foreign ministry said.
- 'Barbaric attacks' -
"Another heinous Russian attack against Kyiv," European Commission chief Ursula von der Leyen posted on X. "Putin's disregard for international law reaches new heights."
In the absence of the Russian ambassador in Lisbon, the charge d'affaires of the Russian Federation has been summoned to be presented with a formal protest, the Portuguese government said.
"These are barbaric attacks on diplomatic institutions, this is crossing all possible red lines and international rules," foreign ministry spokesman Georgiy Tykhy was quoted as saying by Ukrainian agency Interfax.
The Kyiv National Linguistics University said on its Instagram account that its building had also been hit.
Victoria, a 35-year-old doctor, had come out to look at the charred cars and buildings with blown-out windows at the site of an attack.
"Russians should burn in hell," she said.
Air Force spokesman Yuriy Ignat said Ukraine Patriot air-defence systems had been deployed to shoot down the missiles.
- More strikes -
Moscow claimed responsibility for the overnight attack on Ukraine, carried out a day after Russian leader Vladimir Putin threatened to strike Kyiv.
"You know that such strikes on Russian territory have been carried out, and you know that the president has said that every time there will be a response," said Kremlin spokesman Dmitry Peskov.
The Russian defence ministry announced "a combined strike with long-range precision weapons" in response to Ukraine's earlier attack.
The ministry said it had targeted an office of the SBU security service and a defence industry site. "All the targets have been struck," it added.
- 'Dumbass' -
Putin, at a press conference Thursday, had suggested a "high-tech duel" over Kyiv to test his claims that Russia's new hypersonic ballistic missile, dubbed Oreshnik, is impervious to air defences.
"Let them set some target to be hit, let's say in Kyiv," he said.
"They will concentrate there all their air defences. And we will launch an Oreshnik strike there and see what happens."
Zelensky hit back, saying: "People are dying and he thinks it's 'interesting'... Dumbass."
Russian attacks also killed two people in Ukraine's southern city of Kherson Friday.
"Today Kherson woke up from numerous strikes of the Russian army. The occupants have created hell in the city," governor Oleksandr Prokudin said.
Prokudin also said shelling had cut power to 60,000 homes in the region, under daily strikes since Ukraine liberated the city in November 2022.
Russian forces have been pushed back to the other side of the Dnipro river, but the city of Kherson is within range of Russian artillery.
A Russian sabotage group tried but failed to cross the Dnipro during the shelling, spokesman for the Southern Defence Forces Vladyslav Voloshyn told state-run Suspilne media.
Russian troops are on the offensive again, especially in the eastern Donbas region, where this week they captured two small villages near the city of Pokrovsk.
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