Appearing as part of a roundtable on NBC's "Meet the Press," Axelrod said it was "absurd" for Weiner to stay in the race.
"It's time for him to go away," Axelrod said. "He is wasting time and space. Americans believe in second chances, but not third chances."
Axelrod's comment comes on the heels of Weiner losing a key piece of his team. Campaign Manager Danny Kedem quit over the weekend, with Weiner confirming the news to NY1 on Sunday.
"He did a remarkable job," Weiner told the outlet.
HuffPost Pollster's compilation of 19 polls tracking the New York mayoral race still finds Weiner neck-and-neck in the Democratic primary. with City Council Speaker Christine Quinn. Despite the emergence of more details this week surrounding his sexting scandal, Weiner has vowed to stay in the race.