The differences emerged during a commission on secularity which will decide if new legislation is needed to handle a growing debate over religion in schools.
An outcome is expected as early as next month, although a definite date has yet to emerge.
Social Affairs Minister Francois Fillon told the panel he was "favourable to a law forbidding the ostentatious wearing of any religious sign".
His view, he said, was based on France's strict secular tradition in the public sector and in the interests of integrating immigrants by instilling French values.
But Education Minister Luc Ferry said "to tackle 10 contentious cases a year, it's maybe going a bit overboard to create a specific law".
Instead, he and his schools minister, Xavier Darcos, said a future law should "positively affirm the principle of secularism".
France's 60-million strong population counts around five million Muslims, and tensions in some schools have risen recently with teachers ordering Muslim girls to take off their scarves or leave the class.
Ferry estimated there were around 100 cases a year of disputes in schools over the scarves, with about a dozen of those cases turning into lawsuits.
He admitted some principals had been handling the issue themselves, without notifying higher authorities, because they understood that "this would create problems for them".
In an effort to get around the banning of the scarves in state schools, a private Muslim high school opened in the northern city of Lille this month with 12 students.
The six girls in the Lycee Averroes all wear veils.
French Muslim groups say the scarf ban is an attack on Islamic culture which alienates Muslims from French society rather than endears them to it.