Mariupol Mayor Vadym Boychenko said Thursday that no matter what Russia or President Vladimir Putin says about his city, it "is and will be a Ukrainian city." 

Boychenko made the remark hours after Putin ordered his troops not to storm the last remaining Ukrainian stronghold in Mariupol, a steel factory, and claimed victory over the entirety of the city. 

"Whatever statements are made – the city is and will be a Ukrainian city," Boychenko said, appearing to brush off Putin’s assessment of the situation. 

Local residents walk past a destroyed apartment building in Mariupol on Wednesday.

Local residents walk past a destroyed apartment building in Mariupol on Wednesday. (REUTERS/Alexander Ermochenko)

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"We ask for a cease-fire at least for one day for us to be able to make announcements to those residents of Mariupol hiding in shelters and [in] Azovstal," Boychenko added, referencing the steel factory where Ukrainian troops and civilians have been holding out against the invading forces. "For them to leave to some place and our warriors will also leave with their weapons." 

Boychenko said around 100,000 residents remain in Russian-occupied areas of Mariupol, noting that more than 100,000 have managed to evacuate. More than 20,000 have been killed and over 40,000 have been deported to Russia, he added. 

He also said Thursday that between 300 and 1,000 civilians are taking cover inside the steel factory. 

Smoke rises above the Azovstal Iron and Steel Works factory on Wednesday. 

Smoke rises above the Azovstal Iron and Steel Works factory on Wednesday.  (REUTERS/Alexander Ermochenko)

Oleksiy Arestovich, a Ukrainian presidential adviser, claimed Thursday that Putin called off the storming of the factory because "they cannot physically capture Azovstal," according to the Associated Press. 

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Russian military vehicles move on a highway in an area controlled by Russian-backed separatist forces near Mariupol, Ukraine, on Monday.

Russian military vehicles move on a highway in an area controlled by Russian-backed separatist forces near Mariupol, Ukraine, on Monday. (AP/Alexei Alexandrov)

"Completion of military actions on liberation of Mariupol is a success," Putin said Thursday in a televised meeting in Moscow. "Congratulations." 

"Block this industrial zone in such a way that even a fly could not fly through," Putin told Defense Minister Sergei Shoigu. 

Fox News’ Tyler O’Neil contributed to this report.