Kyiv city officials reported fires and fallen debris in several parts of the Ukrainian capital, after AFP journalists heard explosions overnight.
The police said 15 people were injured in Kyiv itself and two more in the surrounding region.
Officials said five civilians were killed by Russian strikes in the Kharkiv and Donetsk regions.
The Russian military meanwhile said Ukraine had targeted it with 788 drones and missiles since Tuesday.
Dozens of drones targeting Moscow have been shot down over the past week.
The attack on Kyiv came hours after Russia and Ukraine completed the first stage of a prisoner exchange agreed at talks last week in Istanbul which, if completed, would be the biggest swap since the start of the conflict.
Both sides received 390 people in the first stage and are expected to exchange 1000 each in total.
Russia has signalled it will send Ukraine its terms for a peace settlement after the swap, which is set to continue over the weekend - without saying what those terms would be.
‘First stage’
The two enemies have held regular prisoner swaps since Russia launched its 2022 offensive but none have been on this scale.
An AFP reporter saw some of the formerly captive Ukrainian soldiers arrive at a hospital in the northern Chernigiv region, emaciated but smiling and waving to crowds waiting outside.
After they stepped off the bus, tearful relatives rushed to embrace the soldiers while others held pictures of their loved ones, hoping to find out if they had been seen in captivity.
Many of the soldiers were draped in bright yellow and blue Ukrainian flags.
“The first stage of the ‘1000-for-1000’ exchange agreement has been carried out,” Ukrainian President Volodymyr Zelenskyy wrote on X.
“Today – 390 people. On Saturday and Sunday, we expect the exchange to continue.”
Russia said it had received 270 Russian troops and 120 civilians, including some from parts of its Kursk region captured and held by Kyiv for months.
The two sides have not yet revealed the identities of those exchanged.
US President Donald Trump earlier congratulated the two countries for the swap.
“This could lead to something big???” he wrote on his Truth Social platform.
Trump’s efforts to broker a ceasefire in Europe’s biggest conflict since World War II have so far been unsuccessful, despite his pledge to rapidly end the fighting.
One of the soldiers formerly held captive, 58-year-old Viktor Syvak, told AFP he was delighted to be back.
Captured in the Ukrainian port city of Mariupol, he had been held for 37 months and 12 days.
“It’s very vivid. I didn’t expect such a welcome. It’s impossible to describe. I can’t put it into words. It’s very joyful,” he said.
Diplomatic push
Several Ukrainians told AFP they were anxiously waiting to see if their relatives had been included in the swap.
“We have been looking for our son for two years,” said Liudmyla Parkhomenko, a mother of a Ukrainian soldier who went missing during combat in the city of Bakhmut.
“Today I would like the Lord to send us good news... We feel in our hearts that he’s alive,” she said.
After 39 months of fighting, thousands of POWs are held in both countries.
Russia is believed to have the larger share, with the number of Ukrainian captives held by Moscow estimated to be between 8000 and 10,000.
With Kyiv not knowing the fate of thousands, each exchange brings surprises, a senior official told AFP.
“Almost every exchange includes people no one had knowledge about,” he said.
“Sometimes they return people who were on the lists of missing persons or were considered dead.”
Diplomatic efforts to end the conflict have stepped up a gear in recent weeks, but the Kremlin has shown no sign it has walked back its maximalist demands for ending the fighting.
Trump has been seeking to broker an end to the fighting since taking office in January, but has failed to extract any major concessions from the Kremlin.
Moscow has defied European pressure for a full and unconditional truce in Ukraine, pressing on with its three-year offensive, which has left tens of thousands dead.
– Agence France-Presse
