"I alone bear responsibility, they can come and get me. I answer to the French people," Macron, who has yet to speak on the crisis, was quoted as saying.
The lawmakers said on Twitter that the French leader had unexpectedly made the remarks at gathering of members of parliament from his party.
>> Read more: France's Benalla Affair: Timeline of of an Élysée Palace scandal
Macron is under fire in the biggest crisis of his tenure after footage emerged of the head of his security detail, Alexandre Benalla, hitting a male protester and dragging away a woman, while off duty and wearing a riot helmet and police tags.