Sanders' campaign sought a recanvass of 25 precincts and three satellite caucuses while Buttigieg's campaign sought a recanvas of 66 precincts and all satellite caucuses.
The Buttigieg request states that the number of state delegate equivalents awarded from satellite caucus locations was "miscalculated and misreported" and a recanvass would result in a net increase of 14 SDEs.
Sanders' campaign said the Vermont senator would receive one additional national delegate if the "errors" in the results are corrected.
On Sunday, the Iowa Democratic Party on Sunday announced it had updated its results, awarding Buttigieg -- the former mayor of South Bend, Ind. -- 14 national delegates and Sanders 12 after applying revisions from 55 precinct reports.
Iowa Democratic Party Chairman Troy Price said he could not say exactly how long the recanvass would take and presented the possibility campaigns could seek a recount if they are unsatisfied with the results of the recanvass.
"While a recanvass is just the first step in the process and we don't expect it to change the current calculations, it is a necessary part of making sure Iowans can trust the final results of the caucus," Sanders senior adviser Jeff Weaver said. "Our volunteers and supporters worked too hard and too many people participated for the first time to have the results depend on calculations that even the party admits are incorrect."