Anti-racism campaigners branded the calls, by EPP group leader Manfred Weber and Ukip leader Paul Nuttall, as political point-scoring.
The UK Independence Party has included the proposed ban in its manifesto for the upcoming general election in the UK in June.
The European People's Party adopted the measure as an official policy at its recent annual congress in Malta, claiming that the ban should be introduced "both for reasons of security and because seeing one another's faces is an integral part of human interaction in Europe."
Weber, speaking recently, said, "We want a total ban of face covering in the EU."
Alfiaz Vaiya, coordinator of the European Parliament anti-racism and diversity intergroup (ARDI), has bitterly attacked the idea.
Vaiya told this website, "A ban on the niqab serves no purpose other than to gain political points. The number of Muslim women wearing the niqab is actually rather low, a minority within a minority.
"The ban on the niqab specifically targets Muslim women and can be considered counterproductive as it further antagonises and targets the Muslim community and in particular Muslim women in Europe.
"If we want to have a more integrated and cohesive society then the best response would be to focus on combatting structural discrimination and prejudices many Muslim women face that prevent them from being able to participate in general society.
"All of this comes at a time when we are arguing for full equality for women and for women to choose for their own bodies."
France was the first country in Europe to ban Islamic face veils, such as the burka and the niqab, in public places.
The controversial ban took effect in April 2011 and made it illegal for Muslim women to leave their homes with their faces covered.
MPs in the Netherlands have voted to ban the burka on public transport and in places such as government buildings, schools and hospitals.
There is also a similar ban in Belgium and German Chancellor Angela Merkel has called for a burka ban wherever legally possible for the "good of Germany".