Speaking at a press conference, Díaz said that a ban on burqas could be included in the final version of Spain's draft Citizen Security Law, Spain's 20 minutos newspaper reported.
The draft bill, yet to be passed in the country's parliament, already includes provisions banning people from hiding their faces in demonstrations, Díaz noted.
Now could be a "good moment" to look to obtain "a level of consensus" on this issue, the interior minister noted.
Díaz stressed his department had no powers when it came to issues affecting the dignity of women, but could rule against the wearing of burqas and other full face veils on the grounds they made identification of people difficult.
"I don't want to say a ban is necessary, " the minister said, but repeated this could be "a good moment" to consider such a prohibition.
Riay Tatary, the head of Spain's Islamic federation, the CIE, responded by saying the ban was "unnecessary" as use of the garment was not widespread in Spain.
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The government of Spain's Catalonia region on Tuesday set in motion plans for a planned law controlling the wearing of burqas and other face-covering attire in public spaces "for reasons of public safety".
The region are pushing ahead with the move, first mooted in 2013, after the EU ruled in July that banning full face veils in public did not violate the human rights of Muslim women.