(Updates casualty figure, adds detail on strikes)
By Pavel Polityuk and Valentyn Ogirenko
KYIV, June 26 (Reuters) - Russian missiles struck a residential building and the compound of a kindergarten in central Kyiv on Sunday, killing one person and wounding six more, officials said, as Moscow stepped up its air strikes on Ukraine for a second day.
Firefighters put out a fire in a badly damaged nine-storey residential building in the central Shevchenkivskiy district, the emergency services said. Debris was strewn over parked cars outside a smouldering building with a crater in its roof.
"They (rescuers) have pulled out a seven-year-old girl. She is alive. Now they're trying to rescue her mother," Kyiv's mayor Vitali Klitschko said
"There are people under the rubble," Klitschko said on the Telegram messaging app. He added that several people had been hospitalised.
Deputy Mayor Mykola Povoroznyk later updated the casualty toll to one person killed and at least six wounded and said the missile struck near the site of a similar attack in late April.
About 400 metres away, a Reuters photographer saw a large fresh crater by the playground of a private kindergarten that had smashed windows. Some privately-held storage garages in the area were completely destroyed.
Blasts were heard in other parts of Kyiv on Sunday, but these were the sound of air defence destroying other incoming strikes, the deputy mayor said on national television.
There was no immediate comment from Moscow, which denies targeting civilians.
Russia's defence ministry said it had used high-precision weapons to strike Ukrainian army training centres in the regions of Chernihiv, Zhytomyr and Lviv, an apparent reference to strikes reported by Ukraine on Saturday.
A Ukrainian air force spokesperson said between four to six long-range missiles were fired on Sunday from Russian bombers more than a thousand kilometres away in the southern Russian region of Astrakhan that looks out onto the Caspian Sea.
Ukrainian Foreign Minister Dmytro Kuleba said Group of Seven countries at a three-day summit should respond to the attack by ramping up sanctions on Russia and providing more heavy weapons to Ukaine.
The last major strike on Kyiv was on June 5 when a rail car repair facility was hit on the outskirts. In late April, a Radio Liberty producer was killed in a strike that hit the building she lived in.
The Shevchenkivskiy historic district is home to a cluster of universities, restaurants and art galleries.
Russia abandoned an early advance on Kyiv in the face of fierce resistance bolstered by Western arms.
Since then Moscow and its proxies have focused on the south and Donbas, an eastern territory made up of Luhansk and its neighbour Donetsk, deploying overwhelming artillery in some of the heaviest ground fighting in Europe since World War Two. (Reporting by Pavel Polityuk, Valentyn Ogirenko, Alessandra Prentice; Writing Lidia Kelly and Tom Balmforth; Editing by Michael Perry, David Clarke and Toby Chopra)