"We understand their desire to honour their friends' memory, but we believe that a competitive arena, where the atmosphere is one of celebration, is not the right place to do it," the IOC's press spokesperson Emmanuelle Moreau told VG on Sunday.
"With 2,800 athletes, there are unfortunately many who have lost friends and loved ones. We understand your grief, but we do not want to allow the competition to become a place of mourning."
Marit Bjørgen and Heidi Weng on Saturday said they had raced for the family of bereaved teammate Astrid Uhrenholdt Jacobsen, whose brother died on the eve of the Sochi Games.
Vidar Løfshus, the team's coach, said that they had been aware that the armbands might infringe IOC rules.
"We were aware of this before we did, so it was a risk we took. We had a desire to do this and felt it was right," he said.
Rule 50 of the Olympic Charter states that "no kind of demonstration, political or religious", should appear on athletes' clothing or equipment.
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Thorvall Johaug, whose daughter Therese raced on Saturday, said he found the IOC's reaction "surprising".
"It's surprising that they react to this. You'd think it was value that meant more than sport," he said. "The commemoration didn't bother anyone."