Ukraine says Russia has carried out a massive missile attack on the capital Kyiv, with at least 13 people injured from the debris of intercepted missiles.

Ukraine's air force says it shot down 31 missiles Russia fired at Kyiv and elsewhere early on Thursday morning.

It says the destroyed missiles included a Kinzhal fired from Russia's Tu-95 strategic bomber. Moscow says the Kinzhal is a hypersonic weapon.

Kyiv Mayor Vitali Klitschko said debris from intercepted missiles fell onto the grounds of a kindergarten, and hit a home, causing a fire. He said at least 13 citizens were injured.

Meanwhile, apparent cross-border attacks from Ukraine have continued in Russia's western Belgorod region. Russian President Vladimir Putin had suggested retaliation.

Russia's defense minister Sergei Shoigu told a ministry meeting on Wednesday that Ukrainian troops attempted to seize border villages in the Belgorod and Kursk regions.

Shoigu said the Ukrainian forces have lost more than 3,500 troops over the past eight days of fighting. He added that all enemy attacks were successfully repelled.

But Russia's defense ministry said cross-border rocket attacks continued in Belgorod on Thursday again.