By Michel Rose

MONTPELLIER (Reuters) - Former economy minister Emmanuel Macron said on Tuesday that France had sometimes made mistakes in unfairly targeting Muslims, suggesting the country could be less stringent in applying its rules on secularism.

He made his comments at a rally in the southern city of Monpellier, but he again stopped short of saying he would stand in next year's presidential election.

"No religion is a problem in France today," he told the crowd. "If the state should be neutral, which is at the heart of secularism, we have a duty to let everybody practice their religion with dignity."

The comments followed a string of deadly Islamist militant attacks in Paris and Nice in the past year that have focused attention on France's large Muslim and Arab population and their place in its society.

Over the summer, the issue of the full-body "burkini" swimsuit, which some towns tried to ban women from wearing, also fueled tensions.

Macron quit President Francois Hollande's government in August, pledging to "transform France". The former banker, who rose to prominence as an adviser to Hollande and then as a minister, has since said he wanted to take time to collect voters' grievances before deciding to run or not.

But he dropped more hints of his ambitions on Tuesday, concluding his speech by saying: "France is a project, and that's the project I want to take further," before launching into a rendition of the French national anthem.

In three rallies outside Paris, he promoted his so-called "diagnosis" for the country. The initiative was both mocked by critics as a futile marketing ploy to play for time and praised by supporters as a healthy democratic exercise.

Earlier this week, Jacques Attali, a former adviser to late President Francois Mitterrand who groomed Macron for a political career a decade ago, pressed his protege to speed things up.

"I am very impatient, even disappointed to see that he, like most others, is taking so much time to come up with a vision for French society," Attali told French radio RTL.

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In his rallies, he struck an unusually intellectual and philosophical note, even by French standards, quoting at length former Nobel Prize laureates Albert Camus and Andre Gide.

That has not dented his popularity.

In an Odoxa poll published on Tuesday, he gained another three points in October, cementing his position as France's second-most popular politician after conservative former prime minister Alain Juppe.

Friends also dismiss suggestions Macron could be more interested in elections beyond 2017.

"He is not just hoping for a nice score that lays the groundwork for another run in 2022," Marc Ferracci, an economics professor at Sciences Po university and a friend of Macron, told Reuters.

"He's impatient, he's convinced his window of opportunity is now."

(Additional reporting by Jean-Paul Pelissier in Montpellier, Noah Barkin in Berlin and Emmanuel Jarry in Paris; Editing by Angus MacSwan)