City Council Speaker Christine Quinn charged yesterday that the failure of the city’s Board of Elections to provide timely results in Rep. Charles Rangel’s congressional primary last month “threatens the credibility of the democratic process.”

Quinn announced that the council would be holding hearings Aug. 8 to see why it took days to get a reliable count off the voting machines.

“New Yorkers must be able to trust that when they cast a valid ballot, their vote will be counted accurately,” declared Quinn, a mayoral contender in 2013.

The Post reported yesterday that the board has asked Albany to modify the election calendar next year because of fears there won’t be enough time after the primaries to conduct possible runoff elections in the races for mayor, comptroller and public advocate.

If no candidate wins at least 40 percent of the vote, a runoff has to be held two weeks later.