The decision comes after a Los Angeles Times report saying the vice president did not want the ad to run, citing a source close to the VP who said he felt the ad treads on "sacred ground."
"The vice president appreciates that they are trying to help," the person close to the vice president told the LA Times. "But he has seen the ad and thinks the ad treads on sacred ground and hopes they don't run it."
Josh Alcorn, senior adviser to Draft Biden, said the group will honor the VP's wish not to air the ad.
"Nobody has more respect for the vice president and his family than we do. Obviously we will honor his wishes," Alcorn said.
The 90-second ad titled "My Redemption" features audio of Biden describing the 1972 car accident that killed his first wife, Neilia, and his 1-year-old daughter Naomi.
“The incredible bond I have with my children is a gift I’m not sure I would’ve had I not been through what I went through,” Biden says as black and white photos of his young family air on the screen. “By focusing on my sons, I found my redemption.”
The ad received mixed reviews in the political realm. White House Press Secretary Josh Earnest said today the ad was "powerful."
"Vice President Biden's personal story is as powerful as any story in American politics," Earnest said. "What made it particularly effective is they used the words of Vice President Biden. It wasn't somebody else telling his story; it's him telling his own story."