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A loud blast rocked the Ukrainian capital about around 5.15pm GMT, sending emergency vehicles racing to a neighbourhood in an attack that shook Mr Guterres and his team.
Emergency services said one strike hit a 25-storey residential block, partially destroying two floors, while AFP reported that a low-rise building was in flames, with rescuers at the scene.
Twelve fire lorries were called in to put out the blaze, with rescuers confirming 10 people were wounded in the strikes, raising an earlier toll of three.
Kyiv mayor Vitali Klitschko said there had been "two hits in the Shevchenkovsky district", one of which struck "the lower floors of a residential building".
A spokesman confirmed that all of the UN delegation were "safe".
"It is a war zone but it is shocking that it happened close to us," Saviano Abreu, spokesman for the UN's humanitarian office, told AFP.
The attack took place less than an hour after Mr Guterres and Volodymyr Zelenskyy held a joint media briefing 3.5 kilometres from the point of impact.
"Today, immediately after the end of our talks in Kyiv, Russian missiles flew into the city. Five rockets," Mr Zelenskyy said.
"This says a lot … about the Russian leadership's efforts to humiliate the UN and everything that the organisation represents."
He said the attack required "a correspondingly powerful reaction".
Ukrainian Foreign Minister Dmytro Kuleba denounced it as a "heinous act of barbarism", while Defence Minister Oleksiy Reznikov said it was "an attack on the security of the Secretary General and on world security".
The timing was not lost on Mykhaylo Podolyak, a senior aide to Mr Zelenskyy.
"Missile strikes in the downtown of Kyiv during the official visit of Antonio Guterres," Mr Podolyak tweeted.
The day before, he was sitting at a long table in the Kremlin, and today explosions are above his head."
Earlier, on his first visit to Ukraine since Russia launched a full-scale invasion on February 24, Mr Guterres toured towns and villages near Kyiv where Russian forces are accused of killing civilians.
"War is an absurdity in the 21st century. The war is evil," he said after visiting places including Bucha, where dozens of bodies in civilian clothes were found, some with their hands bound and others buried in shallow graves.
Later, alongside Mr Zelenskyy, Mr Guterres admitted the Security Council, in which Russia as a permanent member holds a right of veto, had failed to go far enough in its efforts to "prevent and end" Moscow's war in Ukraine.
"Let me be very clear: the Security Council failed to do everything in its power to prevent and end this war. And this is the source of great disappointment, frustration and anger," he said.