Interior Minister Arseny Avakov said the security forces had successfully brought separatist strongholds in the city “under control”.
Five pro-Russian rebels were reported killed and at least four government soldiers injured in the city.
Rebels elsewhere in the region have confirmed they now have three tanks.
The appearance of the tanks, filmed in various towns in the Donetsk region, sparked a row between Kiev and Moscow, with Ukrainian President Petro Poroshenko protesting to his Russian counterpart, Vladimir Putin.
Russia denied Ukrainian allegations that the tanks had entered Ukraine from its territory.
Hundreds of combatants and civilians have been killed since pro-Russian separatists in the Donetsk and neighboring Luhansk regions declared independence after holding referendums last month, which were deemed illegal by the government in Kiev.
Arsen Avakov said government forces had raised the national flag over Mariupol’s council building. The port city lies on the Sea of Azov in the south of Donetsk region which has changed hands several time during the conflict.
The operation had begun at 04:50, the interior minister added.
Confirming that four soldiers were injured, Ukraine’s National Guard said on its website that its recently formed Dnepr and Azov “volunteer” units were being used in the operation.
A rebel source told Russia’s Interfax news agency that five fighters had been killed. Several charred rebel armored cars could be seen in the streets after the battle.
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