The Russian Emergency Ministry later said that 35 people remained unaccounted for, and it wasn't clear if they were in the building when it collapsed.
Almost 1,400 rescuers were searching for those who could have been buried under debris in temperatures of -17 degrees Celsius (1.4 degrees Fahrenheit), which are forecast to plunge to -24 degrees Celsius (-17 degrees Fahrenheit) overnight.
Officials said the blast ripped through the building at around 0600am local time when many residents were asleep.
"It is in the character of our people, despite New Year's festivities, to keep in mind to think of the dead and wounded at this moment", Putin said.
"We are working carefully because there is a risk that the building will collapse".
Temperatures in Magnitogorsk were expected to plunge to minus 23 Celsius on New Year's night, the biggest holiday of the year in Russian Federation.
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Russian news agency TASS reports that six people have been pulled out of the rubble, of which three died, and that 79 were missing.
In 2015, at least five people were killed when a gas blast damaged an apartment building in the city of Volgograd.
The Soviet-era high-rise was built in 1973 and was home to around 1,100 people.
A total of 110 people were registered as residents of the affected section of the building, regional authorities said. Investigators opened a criminal probe into the accident, with the FSB security service confirming the blast had been the result of a gas explosion.
"The chances are reducing with time", Health Minister Veronika Skvortsova responded curtly when pressed by reporters on the likelihood of finding trapped survivors. Residents were evacuated to a nearby school.
There have been several similar incidents in Russian Federation in recent years due to aging infrastructure and poor safety regulations surrounding gas usage.