The United States on Tuesday urged its citizens to leave Ukraine if they can, warning of an increased possibility of Russian military strikes on capital Kyiv in the coming days around Ukrainian independence day as the war reaches the six-month mark.

The warning followed a ban by the Ukrainian government on celebrations in the capital Kyiv on Wednesday's anniversary of independence from Soviet rule due to fears of attack.

On the battlefield, Russian forces carried out artillery and airstrikes in the Zaporizhzhia region in southeastern Ukraine, where fighting has taken place near Europe's largest nuclear power plant, the Ukrainian military said.

But six months on from Russia's Feb. 24 invasion of Ukraine, and with thousands of deaths and widespread destruction of cities, the conflict is locked in a stalemate.

Russian forces control a large swathe of the south, including along the Black Sea coast, and chunks of the eastern Donbass region. The prospects for peace look almost nonexistent.

Fearing a surge in Russian attacks, the U.S. Embassy in Kyiv on Tuesday urged U.S. citizens to leave if they could.

"The Department of State has information that Russia is stepping up efforts to launch strikes against Ukraine's civilian infrastructure and government facilities in the coming days," the embassy said in a statement.

U.S. citizens should leave Ukraine "now" by their own means if it was safe to do so, it said.

Although it was not the first time the U.S. has issued such a warning, this one was made as Ukraine was due on Wednesday to mark 31 years of independence from Soviet rule.

Meanwhile, Ukrainian President Volodymyr Zelenskyy warned Moscow on Tuesday of a powerful response if Russian forces carry out attacks on or around Ukraine's Independence Day.

Asked at a news conference with visiting Polish President Andrzej Duda about the possibility of a Russian missile strike on Kyiv, he said there was a daily threat of attacks and Ukrainian intelligence was working with foreign intelligence.

"(If they hit us, they will receive a response, a powerful response," Zelenskyy said. "I want to say that each day ... this response will grow, it will get stronger and stronger."

The U.S. warning also followed the killing of Darya Dugina, the daughter of a prominent Russian ultra-nationalist, in a car bomb attack near Moscow on Saturday. Moscow has blamed the killing on Ukrainian agents, an accusation Kyiv denies.

Kyiv is far from the front lines and has only rarely been hit by Russian missiles since Ukraine repelled a ground offensive to seize the capital in March.

Nuclear powder keg

Russian shelling hit the eastern city of Kharkiv – Ukraine's second-largest city – around dawn on Tuesday, regional Governor Oleh Synehubov said. A house had been hit but no one was hurt, he said.

In the south, Ukraine said Russia fired artillery and mounted airstrikes in several towns in the Zaporizhzhia region, where Russian forces captured the nuclear power plant shortly after the start of the invasion.

Artillery and rocket fire near the Zaporizhzhia nuclear reactor complex, on the south bank of the Dnipro River, has led to calls for the area to be demilitarized.

Ukrainians living nearby voiced fears that shells could hit one of the plant's six reactors with disastrous consequences.

"Of course, we are worried ... It's like sitting on a powder keg," Alexander Lifirenko, a resident of the nearby town of Enerhodar, said.

The two sides have traded blame over frequent shelling at the plant. Kyiv accuses Moscow of basing troops and storing military hardware there. Russia denies this and accuses Ukraine of attacking Zaporizhzhia with drones.

Moscow requested a U.N. Security Council meeting be held on Tuesday to discuss the Zaporizhzhia plant, Russian state-owned news agency RIA reported, citing Deputy Ambassador to the U.N. Dmitry Polyanskiy.

Russia sent its troops over the border in what it calls a "special military operation" saying it wanted to demilitarise its neighbor and protect Russian-speaking communities. Ukraine and its Western allies accuse Moscow of waging an unjustified war of aggression.

The Office of the U.N. High Commissioner for Human Rights said on Monday that 5,587 civilians had been killed and 7,890 wounded between Feb. 24 and Aug. 21, mainly from artillery, rocket and missile attacks.

UNICEF, the U.N. children's agency, said at least 972 children have been killed or injured over six months of the war.

"The use of explosive weapons has caused most of the child casualties. These weapons do not discriminate between civilian and combatant, especially when used in populated areas as has been the case in Ukraine," a UNICEF statement said.

Separately, Ukrainian armed forces chief Gen. Valeriy Zaluzhnyi provided what appeared to be the first public Ukrainian military death toll, saying nearly 9,000 soldiers had died in action.

Russia has not said how many of its soldiers have been killed. Ukraine's General Staff has estimated the Russian military death toll at 45,400.

Reuters has been unable to verify military losses.