"Our US ambassador Huntsman to Russia visited a church in Moscow today to offer a prayer for all of those affected by the tragedy," Nauert said on Tuesday.
On Sunday, a fire broke out in the Zimnyaya Vishnya ("Winter Cherry") shopping center in Kemerovo in which 64 people died.
"We will hold the Russian people in our thoughts at this difficult time," she said.
Nauert added that while relations with the Russian government are difficult at present, the event in Kemerovo is a human tragedy and "our hears are with the Russians."
Russian President Vladimir Putin declared a day of national mourning on Wednesday.