Ukraine’s capital, Kyiv, and its second-largest city, Kharkiv, have come under heavy Russian missile attacks, killing at least five people, a day after Vladimir Putin warned that Russia would “intensify” its assault on Ukraine. Explosions were heard in all districts of the Ukrainian capital on Tuesday morning, shaking buildings in the city centre, in the third successive day of airstrikes on Ukraine Footage shared on social media by Ukraine’s interior ministry showed several residential buildings, cars and other civilian infrastructure hit by the missile strikes. The mayor of Kyiv, Vitali Klitschko, said on the Telegram messaging app that an elderly woman had died and at least 41 people had been wounded after the strikes. The Ukrainian president, Volodymyr Zelenskiy, praised western-provided defence systems for saving “hundreds of lives”. “I am grateful to all of our partners who are helping us strengthen our air shield. Every day and night, this helps save hundreds of lives that would have been lost if we didn’t have Patriots and other defence systems,” Zelenskiy wrote on his social media platforms, referring to one of the world’s most capable air and missile defence systems. “The terrorist state must feel the repercussions of its actions,” he added. Zelenskiy said on Tuesday evening he had spoken to the UK prime minister, Rishi Sunak, to discuss “Russia’s continued air terror against Ukrainian cities.” He wrote on social media: “I am grateful to the United Kingdom for its substantial and comprehensive aid in bolstering Ukraine’s air defence, particularly with radars, advanced anti-drone systems, and missiles.” Ukrainian air defences downed all 10 incoming “Kinzhal” missiles fired in the latest attack as well as 59 of the 70 cruise missiles and all three Kalibr cruise missiles, said the army head of the army, Gen Valerii Zaluzhnyi. Kira Rudik, a Ukrainian MP and the leader of the liberal Golos party, shared footage on X of her house in Kyiv, which showed extensive damage after Tuesday’s strikes. “My home is now partially in rubble. I have no windows on one side any more. I have minor injuries but I am alive. The fires are everywhere. Russia you will pay,” Rudik wrote. In Kharkiv, a city 25 miles from the Russian border, one person had been killed and 41 wounded after Russian missile strikes hit the city centre, the local governor said. The strikes came just a day after the Russian president warned Moscow would intensify its assault after a Ukrainian attack on Saturday on the Russian border city of Belgorod. “We’re going to intensify the strikes. No crime against civilians will rest unpunished, that’s for certain,” Putin said on Monday during a visit to a military hospital. Russia escalated its attacks on Ukraine last Friday, launching its largest single attack on the country since the war started, in which at least 41 civilians were killed. The following day, the shelling of Belgorod – which Russian officials blamed on Ukraine – killed more than two dozen people, including five children. Russia has struck back repeatedly. Ukraine’s air force commander said Tuesday’s strikes were a repeat of its 29 December attacks in terms of number and type of missiles. In his remarks to Russian soldiers, Putin said he believed Russia held the “strategic initiative” in the war. “In any case, that is how I am being briefed,” he said. Putin’s recent public remarks have been marked by growing confidence since Kyiv’s failed summer offensive. Delays in US and EU military aid to Ukraine have forced its troops to scale back some military operations, further lifting the mood in Moscow. Putin added that Moscow wanted to end the conflict, which the UN estimated had killed more than 10,000 Ukrainian civilians since February 2022, “as quickly as possible” but “only on our terms”. Tuesday’s strikes on Ukraine triggered new calls from western and Ukrainian officials to secure more funding for the country. The US ambassador in Kyiv, Bridget Brink, wrote on X: “Putin is ringing in 2024 by launching missiles at Kyiv and around the country as millions of Ukrainians again take shelter in freezing temps. Loud explosions in Kyiv this morning. It’s urgent and critical that we support Ukraine now – to stop Putin here.” US Congress last month failed to approve $50bn (£39bn) in fresh security aid for Ukraine as negotiators fell short of a deal, with Republicans demanding a domestic border crackdown. Ukraine is separately waiting to receive a €50bn (£43.5bn) package from the EU, delivery of which has looked uncertain after Hungary blocked the EU from approving the aid. The failure to pass the two funding bills has frustrated Ukrainian officials, who have warned that any change in policy from the west could have a strong impact on the course of the war. “Could things have been different, had US Congress approved the military aid for Ukraine in December?” the Ukrainian MP Lesia Vasylenko wrote on X. The escalating violence came as Zelenskiy said in a combative interview with the Economist that the notion that Russia was winning the nearly two-year-old war was only a “feeling” and that Moscow was still suffering heavy battlefield losses. Zelenskiy urged Europe to continue supporting Ukraine and argued that by doing so, Europe was protecting itself from Russian aggression. “Giving us money or giving us weapons, you support yourself. You save your children, not ours,” he said. He said Ukraine’s priorities in 2024 included hitting Russia’s strengths in Crimea to reduce the number of attacks on his country, and protecting key cities on the eastern front. Zelenskiy rejected suggestions that Russia was willing to negotiate, saying he did not see “any fundamental steps forward to the peace from Russia”. “I see only the steps of a terrorist country,” Zelenskiy said, pointing to Russian missile attacks. The Ukrainian leader acknowledged that his country did perhaps “not succeed [in 2023] as the world wanted. Maybe not everything is as fast as someone imagined”. But he cited heavy Russian losses in the besieged eastern town of Avdiivka, which he visited last week, as evidence that Russia was not “winning”. Later on Tuesday, Russian officials said one man had been killed and seven people wounded in the Russian border city of Belgorod after a Ukrainian attack. The regional governor, Vyacheslav Gladkov, said the man had been killed by a missile that landed next to his car, and that four people had been wounded at a car market.