Buttigieg filed a request for a recanvass of 66 precincts and Sanders for 28 precincts, the party said in a statement.
It said it will review the requests to determine whether they meet the requirements.
Buttigieg had a slim lead over Sanders in the Feb. 3 nominating contest, which took days to settle after a technical meltdown led to delays in determining the winner.
"This is not a PR exercise for us," said Iowa Democratic Party Chair Troy Price on Monday. "This is upholding our core mission, which is delivering a full and complete caucus, and building a coalition to defeat Donald Trump."