The 46-year-old has been provisionally barred from all football activity for an initial 90 days by FIFA while it investigates his conduct at last month's Women's World Cup final in Sydney.
Now, the RFEF's current president Pedro Rocha has written a letter distancing the federation from Rubiales' actions.
“The damage caused to Spanish football, to Spanish sport, to Spanish society and the values of football and sport as a whole have been enormous,” Rocha's letter said.
“Mr Rubiales' actions do not represent the values defended by the Spanish federation, nor the values of Spanish society as a whole.
“His actions must be attributed solely and exclusively to him, since he is the one solely responsible for those actions before society, before the sports governing bodies and, if applicable, before justice.
“To be clear, this position was that of Mr Rubiales, not that of the RFEF. We feel especially sorry and ashamed for the pain and additional distress this has caused.”