The women quoted by the Mediapart story on Saturday said Abad had forced them to have unwanted sexual relationships with him. The actions happened in late 2010 and early 2011, they said.
One of the women filed a complaint to the police against Abad in 2017 which was closed without further action, Abad and Mediapart said.
"I contest with the greatest force these accusations of sexual violence," he said in a statement sent to Reuters. "The sexual relations that I have had throughout my life have always been by mutual consent."
Abad said his disability, a disorder called arthrogryposis that affects all four of his limbs, made it physically impossible for him to commit the acts he was accused of.
Abad joined the government formed on Friday after President Emmanuel Macron's re-election.
Asked to comment on the accusations against Abad, Prime Minister Elisabeth Borne said she was not aware of them when he joined the government.
"I will be very clear: on all these subjects of harassment, sexual assault, there can be no impunity and we must continue to act so that women who may be victims of assault, harassment, can speak freely," she said.
Borne said her government would bear the consequences of appointing Abad, "if there are new elements and a new case is opened." She did not give more details. (This story refiles to show Mediapart story was published on Saturday)
(Reporting by Sybille de La Hamaide and Elizabeth Pineau; editing by Frank Jack Daniel)