Led by Georges Fenech, a supporter of former president Nicolas Sarkozy, the group of what is believed to be around 40 lawmakers signed an open letter at a meeting Monday evening explaining that they believed it impossible to continue campaigning until the Fillon affair is regulated.
The letter explained that in the absence of an explanation of how a number of Fillon family members were employed as parliamentary assistants by Fillon, the executive of the party should meet to work out a solution to the ongoing crisis.
The letter was due to be presented to Francois Fillon at a meeting Tuesday. However, Fenech has withdrawn the request for an executive meeting, while Fillon has insisted that there is no other possible candidate.
At a meeting of Les Républicains deputies Tuesday morning, Fillon said that his withdrawal from the campaign at this stage could, in effect, wipe out the party and any chance of winning the presidential election due to take place at the end of April.
"There is no alternative," Fillon told the meeting.
Over the weekend , François Fillon vowed to "fight to the end" at a rally on the Indian Ocean island of Réunion Sunday as a newspaper claimed that judges could order action against him this week.
The embattled French presidential candidate faces allegations that members of his family held fake jobs as parliamentary assistants for him.
"I am being attacked 24 hours a day but I also receive countless messages of support," Fillon told an election rally on Réunion, a French overseas department. "I will fight to the end because my programme is the only one capable of reviving France."
Fillon and his family are under investigation but have not been charged.
The Journal Du Dimanche paper on Sunday cited sources at the French fraud office saying that legal action against Fillon and his wife could be launched this week.