Francois Fillon has called on Muslims to condemn extremists and denounce terrorism and radical Islam
The right-winger said that Muslims could not stand back and watch as jihadis "distorted" Islamic texts and divided communities.
During a visit to the Noor-al-Islam Grand Mosque, Mr Fillon said: "I want all Muslims – including French citizens – to vent their anger at radical Islamists and to protest against the rise of Islamic extremism – not just terrorism.
"Muslims need to start denouncing those who are distorting Islamic texts and condemning those who are trying to divide their community."
The Noor-al-Islam Grand Mosque is located in the Indian Ocean island of La Réunion, a French region. It is France's oldest mosque.
Mr Fillion said radical extremists who categorically refused to adhere to – and did not respect – the values of the French republic should be "banned" from entering France.
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The former prime minister visited the Noor-al-Islam Grand Mosque in La Réunion
He said: "Here in La Réunion, Muslims and Christians co-exist peacefully; the same, however, cannot be said for mainland France.
We need a liberal 'Islam of France' that is free from foreign influence
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"Radical, totalitarian Islamists are committing atrocities in the name of Islam and are trying to monopolise the Muslim faith. They must be stopped."
The former prime minister – who has pledged to clamp down on radical Islam throughout his campaign – added that the French Council of the Muslim Faith (CFCM) – the main umbrella group for mosque associations – should be "more about religion, and less about politics".
He said radical extremists who adhere to French values should be 'banned' from entering France
Mr Fillon added that, if elected president, he would ban Muslim countries from financing French mosques.
He said: "We need a liberal 'Islam of France' that is free from foreign influence. Some religious leaders are driven by politics: they do not have Muslim worshippers' best interests at heart."
Mr Fillon, who is fighting to save his presidential bid after being accused of paying his wife hundreds of thousands of euros in taxpayers' money for a 'fake job' as his parliamentary assistant, added that he was "religious man" who wanted to "protect all religions".
The right-winger has pledged to clamp down on radical Islam throughout his campaign
He said: "Freedom of religion is a fundamental right that I have vowed to protect. I also believe in a 'softer' brand of secularism."
Earlier that day, Iqbal Ingar, the president of the mosque, urged French officials, including Mr Fillon, to "lead by example" and to "come to the defence" of moderate Muslims, who, according to Mr Ingar, are being "tarred with the same brush as radical Islamists".
He said: "Presidential candidates must bring citizens closer together; they should not be driving a wedge between Muslims and non-Muslims.
"France is at war with extremism and terrorism, but not with Islam. Officials need to make that clear."
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