Kyiv has been through the worst of the fighting since Russia invaded Ukraine on February 24, but the Russian military is slowly closing in on the city and the shelling has intensified.
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Several apartment blocks have been struck by Russian forces based outside the city.
At least two people were killed in the latest strikes, Mr Klitschko said.
Shelling ignited a huge fire at a 15-storey apartment building and a frantic rescue effort was underway to rescue the several people trapped inside.
Shockwaves from an explosion also damaged the entry to a downtown metro station that has been used as a bomb shelter.
City authorities tweeted an image of the blown-out facade, saying trains would no longer stop at the station.
"The capital is the heart of Ukraine and it will be defended," Klitschko said.