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"To have European parliamentary elections three years after the country voted to leave would be damaging to our politics as a whole," Stephen Barclay told parliament on Thursday.
But such a prospect could not be ruled out, he said.
"If we are a member of the European Union, then under treaty law we will be required to have European parliamentary elections," Barclay said.
Prime Minister Theresa May has said she does not want Britain to take part in the elections but that might happen if she has to extend Brexit beyond its latest scheduled date of April 12.