DUP MP Sammy Wilson has likened those calling for a second EU referendum to fascists.
While the UK voted in favour of Leave in the recent referendum, the majority of Northern Ireland votes opted for Remain.
The DUP was the only major party in Northern Ireland that backed the Leave campaign.
In the wake of the result millions of people signed a petition calling for a second EU Referendum.
While in Northern Ireland another petition was launched calling on the Northern Ireland Assembly to refuse consent to leave.
On Monday morning speaking on the BBC Stephen Nolan show DUP MP Sammy Wilson likened those calling for a second Referendum to "fascists".
He said: "It really does annoy me.
"These people in my view, are little short of fascists
"They don't wish to have the democratic wishes of the people honoured.
He continued: "That's what fascists do. They wish to have only their views."
He added: "The decision was made that this was a decision which should be taken by a referendum. Politicians voted for legislation in the House of Commons as to the nature of the Referendum.
"The questions to be asked in the Referendum who would be eligible to vote.
"Having had the Referendum just because you don't like the result doesn't mean you then say it's not valid.
"What does annoy me is it is driven by people who would regard themselves as the elite in society - who have total disregard for the views of ordinary people."