The DUP's Brexit spokesman hit back at Julia Hartley-Brewer after the presenter likened ongoing Brexit negotiations to "a game of chicken".
During the exchange on the breakfast show, Sammy Wilson said the situation was "much too serious" to be compared to the game.
"The implications are much too serious for Northern Ireland, and indeed the UK as a whole, to simply reduce this to a game of chicken," Mr Wilson said.
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The pair had been discussing the impasse reached by the EU, the Irish government and the UK, particularly in relation to a hard border forming in Ireland.
"It's quite clear now as we approach March 29 that the Irish government recognises the implications of no-deal for their economy, the EU recognise they're going to have to either demand changes from Ireland, which Ireland doesn't want to accept, or else back down on the backstop insistence which they have had so far," he said.
'Go in with a strong hand'
"It's quite right for the government of the UK, now that there's the EU and Irish government at sixes and sevens to exploit that, and move in with an alternative plan for dealing with cross-border trade."
He added: "It is quite clear that there is some panic within the Irish government and the EU. Now is the right time for the Prime Minister to go in with a strong hand."