"No… I was a democratically elected candidate, I gathered 1,500 elected representatives' signatures. No one has the power to make me quit the election, and I see no reason to withdraw my candidacy," Fillon stated.
He added that he hoped to convince his fellow party members that only his project had any chance of garnering sufficient support in the upcoming election.
The comments came after Fillon's supporters gathered in Paris in their thousands. The Republicans party has been looking into options for resolving the penelopegate scandal.
The center-right candidate has repeatedly denied all accusations and pressed on with his election campaign despite a dip in popularity. His party has been pressed to look for alternatives for his candidacy, with his former primaries rivals among those rumored to be up for replacing him.
Fillon has called the media storm a "political assassination." He is expected to face investigators on March 15, after which formal charges may be made.
The first round of the French presidential election is scheduled for April 23, with the run-off set for May 7.