At least 520 people were injured, more than 60 of them had serious injuries, the Tianjin government said on its Weibo microblog, and the People's Daily newspaper said four fires were still burning, the report said.
China Central Television (CCTV) had earlier put the death toll at 17. Tianjin authorities later said 12 firefighters were among the 44 killed.
The official Xinhua news agency said 1,000 firefighters and more than 140 fire engines were struggling to contain a blaze in a warehouse that had "dangerous goods".
Several fire trucks had been destroyed and nearby firefighters wept as they worked to extinguish flames, the Beijing News reported.
Despite the devastation, the port was operating normally, a port official said. Tianjin port is the gateway to northern China's industrial belt.
Xinhua said the explosions, the first equivalent to 3 tonnes of TNT and the second to 21 tonnes of TNT, ripped through the warehouse.
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According to an assessment by government environmental inspectors published in 2014, the facility was designed to store several dangerous and toxic chemicals including butanone, an explosive industrial solvent, sodium cyanide and compressed natural gas.
CCTV said at least one person at a "relevant company" had been detained.
