The authorities had not been able to start a rescue operation because of street fighting and continued Russian shelling nearby.
Earlier, Mariupol city hall cited a similar death toll in a Telegram post.
“From eyewitnesses, information is emerging that about 300 people died in the Drama Theatre of Mariupol following strikes by a Russian aircraft,” officials wrote.
Mr Andryuschenko also confirmed that fighting was continuing in the middle of the city, but insisted that Russian forces had not yet managed to take control of the city.
The port city of Mariupol is key to Russia’s military campaign. If it falls, it would give Russia control of one of Ukraine’s biggest ports and create a land corridor between Crimea and the Russian-backed regions of Luhansk and Donetsk.