Justice Secretary David Gauke has survived a no-confidence vote by his constituency Conservative Association.
Mr Gauke represents South West Hertfordshire and opposes a no-deal Brexit.
Political campaign group Leave.EU tweeted it wanted to “claim our first Cabinet scalp”.
The no-confidence motion was defeated 123 to 61. Mr Gauke tweeted he was “grateful to the members of my association for their support”.
The closed meeting was held at Kings Langley Community Centre and lasted for more than two and a half hours.
The Justice Secretary tweeted immediately after the result “a no deal would be immensely damaging to the UK”.
He also called for his party to “be a broad church”.
Prior to the vote he received support from many of his Cabinet colleagues, including Work and Pensions Secretary Amber Rudd who tweeted: “Tonight’s motion of no confidence in David Gauke is ludicrous.
“Rounding on colleagues in this way is the type of behaviour you’d expect from the hard left.”
Leave.EU replied to Ms Rudd saying: “Thanks for your feedback, Amber. You’re next.”
Energy Minister Claire Perry tweeted the Leave.EU “hit list ignores the fact that MPs like David have voted repeatedly for a firm EU exit – if other MPs had joined us rather than indulging in their Brexit fantasies we would be out by now”.
Pro-Remain Conservatives Phillip Lee and Dominic Grieve, the former attorney general, received votes of no confidence from their local associations earlier this year.