"This fight is in your hands from now on. I have no right to fight with you anymore," Fillon said in front of the leaders of The Republicans, as quoted by the BFMTV broadcaster.
Fillon reportedly added that he would have to rethink his life, help his family recover.
In late January, a scandal broke out around Fillon possibly employing his wife and two children within parliament and the amount of work done by them was questioned by the media and investigators. The scandal largely overshadowed Fillon's presidential campaign.
The legislative elections will be held in France in June.