Sanders told reporters it was "highly inappropriate" to debate the chief of staff over his statement, given that he is a retired four-star Marine general.
"If you want to go after General Kelly, that is up to you," she said. "If you want to get into a debate with a four-star Marine general, I think that is something highly inappropriate."
Kelly erroneously claimed Thursday that Rep. Frederica Wilson, a Florida Democrat, had taken credit for funding a new FBI building in Miami. Kelly's comment, which was meant to defend President Donald Trump's condolence call that upset the family of a fallen solider, was disproved by a video of Wilson's speech.
After her comments about the propriety of contesting Kelly's statements caused a stir, Sanders said in an email comment to CNN: "Of course everyone can be questioned. But after witnessing General Kelly's heartfelt and somber account, we should all be able to agree that impugning his credibility on how best to honor fallen heroes is not appropriate."
Kelly served as the commander of United States Southern Command for four years under President Barack Obama and served as a commanding general in Iraq from 2008 to 2009. His appearance in the briefing room on Thursday sought to lend credibility to the discussion over Gold Star families, given that Kelly's son Robert died when he stepped on a landmine in Afghanistan in 2010.
Sanders said the chief of staff stands by his comments despite the video.
"Absolutely," she said at the briefing, adding that Wilson -- who is known for regularly wearing colorful cowboy hats -- is "all hat, no cattle."
Sanders added that Kelly's interpretation was developed by "a few comments that day that weren't part of that speech and weren't part of that video." White House aides did not respond when CNN asked if they could make those examples public.
Sanders said Kelly's statement Thursday "should have ended yesterday after Gen. Kelly's comments, but it it didn't."
President Donald Trump, according to a source who spoke with him after Kelly's performance, said he was pleased with the way his chief of staff defended his call to a Gold Star widow. The source added that Trump thought Kelly was fantastic and continued to praise his performance Friday.