Ukraine, meanwhile, has reported the deaths of almost 9000 military personnel since its territory was invaded six months ago.
Near frontlines in the south of the country, Ukraine said Russia fired rockets into several towns north and west of Europe's largest nuclear power plant.
The plant was captured by Russian forces shortly after they invaded Ukraine on February 24.
Artillery and rocket fire near the Zaporizhzhia nuclear complex, on the south bank of the Dnipro River, has led to calls for the area to be demilitarised.
Ukrainian President Volodymyr Zelenskiy has warned Moscow could try "something particularly ugly" in the run-up to Wednesday's 31st anniversary of independence, which also marks half a year since Russia invaded.
Kyiv is far from the front lines and has only rarely been hit by Russian missiles since Ukraine's troops repelled a ground offensive to seize the capital in March.
But authorities in the city have banned public events related to the anniversary from Monday until Thursday due to the possibility of renewed rocket attacks, a document showed.
Other jurisdictions have also restricted public gatherings.
In Kharkiv, a northeastern city that has come under frequent longer-range artillery and rocket fire, Mayor Ihor Terekhov announced an extension to an overnight curfew to run from 4 pm to 7am.
In the port of Mykolaiv near Russian-held territory to the south, regional governor Vitaliy Kim said authorities urged people not to gather in large groups.
In his regular evening address, Zelenskiy called for new punitive measures on Russia from Europe, which is bracing for energy shortages after Moscow announced a three-day halt to some gas flows to the continent in apparent retaliation to European Union sanctions.
Russia denies this, blaming the cuts on the sanctions themselves and various technical problems.
"The only question is how many lives Russia will be able to take before the backlash from the international community becomes really tangible to those who are responsible," Zelenskiy said.
Fears of intensified attacks rose after Russia's Federal Security Service on Monday accused Ukrainian agents of killing Darya Dugina, the daughter of a Russian ultra-nationalist ideologue who was close to President Vladimir Putin, in a car bomb attack near Moscow.
Ukraine denies involvement.
The two sides have also traded blame over frequent shelling at the Zaporizhzhia nuclear plant, where Kyiv accuses Moscow of basing troops and storing military hardware.
Russia denies this and accuses Ukraine of targeting Zaporizhzhia with drones.
Overnight, Russian forces fired rockets into the nearby towns of Nikopol, Krivyi Rih and Synelnykovskyi, the area's regional governor, Valentyn Reznichenko, wrote on Telegram.
In Russian-occupied Kherson, the sole bridge across the strategic Dnipro River was hit by high-precision HIMARS rockets supplied to Ukraine by the United States, injuring 15 people, a source in occupied Kherson's emergency services told Russia's Interfax news agency.
The bridge, a key crossing for Russian military transport in the region, has been repeatedly targeted by Ukrainian forces as they stage a counter-offensive to retake the region.
The UN's human rights commission said on Monday 5587 civilians had been killed and 7890 wounded between February 24 and August 21, mainly from artillery, rocket and missile attacks.
UNICEF said at least 972 children have been killed or injured.
"The use of explosive weapons has caused most of the child casualties," the agency's executive director, Catherine Russell, said in a statement.
"These weapons do not discriminate between civilian and combatant, especially when used in populated areas as has been the case in Ukraine."
Separately, General Valeriy Zaluzhnyi - Kyiv's army chief - provided what appeared to be the first public Ukrainian military death toll, saying nearly 9000 soldiers had died in action.
Russia has not said how many of its soldiers have been killed.
Ukraine's General Staff have estimated the Russian military death toll at 45,400.
Reuters has been unable to verify military losses.
