"Several explosions in Darnytskyi and Dniprovskyi districts of the capital," Kyiv Mayor Vitali Klitschko wrote on the Telegram messaging app on Sunday.
"Services are already working on site. More detailed information - later."
A Reuters witness saw smoke in the city after the explosions.
The Ukrainian claim on Sievierodonetsk could not be independently verified, and Moscow said its own forces were making gains there. But it was the first time Kyiv has claimed to have launched a big counter-attack in the small industrial city after days of yielding ground.
Sievierodonetsk Mayor Oleksandr Stryuk said street fighting continued during the day on Saturday, with both sides exchanging artillery fire.
"The situation is tense, complicated," he told national television, saying there was a shortage of food, fuel and medicine.
"Our military is doing everything it can to drive the enemy out of the city."
Russia has concentrated its forces on Sievierodonetsk in recent weeks for one of the biggest ground battles of the war, with Moscow appearing to bet its campaign on capturing one of two eastern provinces it claims on behalf of separatist proxies.
Both sides claim to have inflicted huge casualties in the fighting, a battle that military experts say could determine which side has the momentum for a prolonged war of attrition in coming months.
Ukrainian President Volodymyr Zelenskiy offered a stark message: "The terrible consequences of this war can be stopped at any moment ... if one person in Moscow simply gives the order," he said, in an apparent reference to Russian President Vladimir Putin.
"And the fact that there is still no such order is obviously a humiliation for the whole world."
Putin will discuss the war in an interview due to be broadcast on national television on Sunday. In a brief excerpt aired on Saturday he said Russian antiaircraft forces have shot down dozens of Ukrainian weapons and are "cracking them like nuts".
Ukraine says it aims to push Russian forces back as far as possible on the battlefield, counting on advanced missile systems pledged in recent days by the United States and Britain to swing the war in its favour.
Russia's defence ministry said its troops were forcing the Ukrainians to withdraw across the Siverskiy Donets River to Lysychansk on the opposite bank.
Tens of thousands of people are believed to have died, millions have been uprooted from their homes, and the global economy has been disrupted in a war that marked its 100th day on Friday.
Ukraine is one of the world's leading sources of grain and cooking oil, but those supplies were largely cut off by Russia's closure of its Black Sea ports, with more than 20 million tonnes of grain stuck in silos.
