Ukrainian President Volodymyr Zelensky has admitted for the first time that his military is conducting an offensive in Russia’s western Kursk region.

In his evening televised address on Saturday, Mr. Zelensky said the Ukrainian military was moving the war “to the territory of the aggressor.”

It came five days after Ukraine launched an operation that caught Russia by surprise and prompted mass evacuations on both sides of the border.

Ukrainian authorities reported that early on Sunday morning Russian aircraft carried out attacks on the country’s capital, Kiev, and the Sumy region.

A 35-year-old man and his four-year-old child died in Kiev, Ukrainian rescue services reported on Sunday.

According to a statement published on the Telegram app, three more people were injured, including a 13-year-old child.

Early Sunday morning, Kyiv Mayor Vitali Klitschko posted on Telegram that air defense units were “acting” and warned civilians to stay in shelters.

In his speech Saturday, Zelensky thanked Ukrainian “warriors” and said he had discussed the operation in Russia with the country’s top military commander, Oleksandr Syrsky.

“Ukraine proves that it is indeed capable of restoring justice and putting the necessary pressure on the aggressor,” he added.

Reports say Ukrainian troops are threatening to capture one regional city as they fight across an area more than 10 km (six miles) deep inside Russia, the biggest advance since Moscow launched a full-scale invasion of Ukraine in February 2022.

At least 13 people were injured, two of them seriously, in Kursk on Sunday morning, said acting regional governor Alexei Smirnov.

More than 76,000 people have been evacuated from the border areas, according to the Russian news agency TASS, and Mr Smirnov said on Sunday he had ordered authorities to speed up operations to ensure the safety of civilians.

Russia’s National Anti-Terrorist Committee on Friday launched an “anti-terrorist operation” in three regions in response to Ukraine’s surprise cross-border invasion.

This means that authorities in the border regions of Kursk, Belgorod and Bryansk can restrict the movement of people and vehicles, as well as use telephone wiretapping, among other things.

Russia said about 1,000 Ukrainian troops, supported by tanks and armored vehicles, entered the Kursk region on Tuesday morning.

According to sources, Ukrainians have already taken over a number of villages and are also threatening the regional city of Sudza.

A video was released on Friday purporting to show armed Ukrainian soldiers claiming to have control of the city as well as a key Russian gas facility owned by Gazprom.

BBC Verify confirmed that the footage was indeed from a Gazprom facility on the northwestern outskirts of Suja, about 7km from the Ukrainian border. The footage itself does not support the claim that Ukrainian troops have taken over the entire town.

Russian military bloggers have previously claimed that the city is under Moscow’s control.

BBC Verify has verified and confirmed the location of another video posted online on Friday morning, which shows a 15-vehicle Russian convoy damaged, burned and abandoned on a road through the town of Oktyabrskoe, about 38km from the border on the Russian side.

The footage also shows Russian soldiers – some wounded, some presumed dead – among the vehicles.

Moscow has since sent reinforcements – including tanks and missile launchers – to Kursk.

In its latest report Saturday morning, the Russian Defense Ministry said Russian troops “continue to repel an attempted invasion” by Ukrainian forces.

He claimed that Ukraine’s attempts to “penetrate deep into Russian territory” had been thwarted.

The Russian claims have not been independently verified.

The UN nuclear agency on Friday urged Russia and Ukraine to “exercise maximum restraint” as fighting approached the Kursk nuclear power plant, one of the largest such facilities in Russia.

International Atomic Energy Agency (IAEA) chief Rafael Grossi said measures must be taken “to avoid a nuclear accident with serious radiological consequences.”

The power plant is located approximately 60 km northeast of Suja.