Thirsk and Malton MP Kevin Hollinrake will be backing Theresa May in tonight's confidence vote.
Mr Hollinrake, who also represents Filey, said: "My colleagues have to use their own judgement and I respect that, however I don't agree with it because whoever is in that position will face the exact same challenges.
"The Prime Minister's deal is the only deal that fulfils the promises of the referendum. It will guarantee friction-less trade, no hard border in Norther Ireland and the end of free movement."
Asked who he believes could replace the Prime Minister, should she lose tonight's leadership contest Mr Hollinrake added: "To me it's not about the person, it's about delivering Brexit and to be honest I don't see anybody who can come up with a better solution to the challenges that we face than the Prime Minister's."
Mr Hollinrake also warned that if Mrs May loses tonight Brexit could be delayed.
He said: "If the Prime Minister loses, we could see weeks of delays or even a general election or a second referendum."
The vote will take place between 6pm and 8pm.
The result will be announced at 9pm.