George Eustice has criticised politicians who "threaten to resign" and "talk about it in the papers".
The former environment minister - and deputy to Michael Gove - handed in his own resignation this week, citing concerns over allowing MPs to delay a vote on Brexit if the Prime Minister's deal is rejected.
Offering advice to fellow ministers considering resignation, Mr Eustice said the "right" way to do it was "privately" and "quietly".
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"People like me on the Brexit side of this debate, we don't believe in going around threatening to resign," he told talkRADIO's Julia Hartley-Brewer. "If you get to a position where you can no longer stay part of a government you just resign..
"You don't threaten to resign and talk about it in the papers. When you can't do it anymore you should just go."
Mr Eustice revealed that Theresa May did not want him to resign, and was "relaxed" about him doing so.
"You make your case and offer your counsel to the Prime Minister, and accept sometimes it won't be followed," he added.