"There is only one reason why this continues: Russia does not want a ceasefire, and we see it. The whole world sees it", writes Zelenskyj on the messaging service Telegram.
Six of the fatalities in Kryvyj Rih are children, according to Governor Serhij Lysak.
Over 50 people, in addition to the fatalities, have been injured in the attack, according to the city's military administration. The number of injured is reported to be increasing.
"A ordinary city"
Unconfirmed video recordings on social media show how a thick smoke cloud rises towards the evening sky. Kryvyj Rih is located in the Dnipropetrovsk region, about six miles from the front line.
"A Russian robot against an ordinary city. Directly on the street. In an area with residential houses", writes Zelenskyj and adds that five houses have been hit.
Zelenskyj urges Ukraine's allies to increase pressure on Russia and continue to support Ukraine militarily.
"Every robot, every drone proves that Russia only wants war", writes the president.
"The USA, Europe, and the rest of the world have enough power to make Russia abandon terror and war."
Drones against Charkiv
Earlier on Friday, reports emerged that at least five people had been killed and around 30 injured in a Russian drone attack against the city of Charkiv.
The Zaporizjzja region in the south and the Kyiv region have also been subjected to Russian attacks.
In Dnipro, a municipal official has been killed in a car bomb attack.
The man died in hospital after the attack on his car, according to the Ukrainian prosecutor's office. His wife was also injured in the attack, which is being investigated as a terrorist attack.
In Russia, one person is reported to have been killed by a Ukrainian drone in a village near the border with Ukraine in the Brjansk region, according to Governor Alexander Bogomaz. Another person is said to have been injured in the attack.