Francois Fillon has vowed that "no one" could force him to quit his bid for the presidency despite calls for him within his own Republican party to step down over an expenses scandal.
The politician is facing corruption allegations over claims that he paid his wife for work that she never did.
But he was in a defiant mood after holding a rally in Paris on Sunday attended by tens of thousands of supporters.
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"No one today can prevent me being a candidate," Mr Fillon said in a TV interview on Sunday night in which he again insisted an investigation into the payment scandal was politically motivated.
"Of course it is aimed at stopping me being a candidate," he added.
The Republican party will meet later today to discuss whether to change their candidate for the presidential election.
Former prime minister Alain Juppe, 71, has been tipped as a likely replacement.
An opinion poll on Sunday found that Mr Juppe would reach the second round if he replaced Mr Fillon.
Earlier at the rally near the Eiffel Tower, Mr Fillon admitted he made mistakes and apologised.
He said: "Even if this charge against me is unjust... I owe you an apology. I made the first mistake, asking my wife to work for me. I should not have done it."
"I made a second mistake by hesitating on how to tell you about it," BFMTV reported the candidate as saying.
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Amid chants of "Fillon! President!", he added: "Thank you from the bottom of my heart for being here, you who have braved bad weather conditions, orders, caricatures, sometimes even insults by coming here on this square with such strong symbols."
His supporters put the audience, which is likely to be used as a measure of support for the beleaguered candidate, at 200,000. Independent experts told BFMTV that the area could hold between 35,000 and 50,000 people.
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On Saturday, Mr Fillon's British-born wife Penelope broke her silence over the "fake jobs" scandal , saying that she had carried out a "lot of different tasks" for her husband.
The Republicans candidate was the frontrunner until mid-January when the Canard Enchaine newspaper claimed he had paid his wife and two of their children nearly €900,000 (£780,000) as parliamentary assistants or advisers.
Opinion polls currently show that far-right leader Marine Le Pen and centrist Emmanuel Macron would go through to the second round of the presidential contest on 7 May, with Mr Fillon eliminated in the first round.
Supporters, including a campaign spokesman and five MEPs from the Republicans party, withdrew their backing this week and called for another candidate to be installed quickly.
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