The commission issued a statement Tuesday saying a Muslim veil ban - now being considered by lawmakers in France and Belgium - would rob women of their freedom of expression and could violate their religious freedoms.
The panel also urged Switzerland to end its ban on the construction of Islam minarets as soon as possible.
The Council of Europe is a 47-nation human rights institution that will discuss the burqa issue at its plenary next month.
It is a separate organization from the European Union and is the region's primary human rights watchdog whose rulings are binding on all Council of Europe member states.
France's opposition Socialists also challenged the plan to ban full Islamic veils in all public places, proposing a milder bill based on practicality rather than values.
The government is expected to present legislation next week to outlaw face-covering veils on the grounds that they are demeaning to women, even though legal experts have warned that such a prohibition could violate religious freedom.
"What we want is efficiency rather than symbolism," Jean-Marc Ayrault, head of the Socialists' group in parliament, told reporters.
The Socialist draft says that everyone must keep their face uncovered when using public services to permit identification.
In practice, this could mean women would have to remove face veils to pick up their children from school, or during wedding ceremonies at town halls.
Several human rights organizations have spoken out against a general prohibition on veils such as the burqa and the niqab.
A committee of the Council of Europe - a European human rights body based in Strasbourg - also said on Tuesday it opposed such a ban, which is being discussed in France as well as Belgium.
The Socialist proposal could circumvent concerns over religious discrimination by focusing on security and pragmatism.
"We believe that banning it from the public sphere... risks stigmatising people and above all being totally ineffective because it would be unenforceable," Socialist leader Martine Aubry told reporters after meeting Prime Minister Francois Fillon to discuss the issue.
But she stressed the Socialists opposed full Islamic veils and did not want them in France.
The Council of Europe committee said full veils "could be a threat to women's dignity,” but women should be free to wear them if they wanted to.
However, the committee said legal restrictions might be justified for security purposes and in certain situations where the wearer's face had to be seen.
The idea of a ban was first floated last year by French mayors who said more and more women were turning up fully veiled at schools and in town halls, and refusing to show their faces even for the purpose of identification.
