The Scottish Conservative leader said her party was free to pursue its own Brexit stance “independently of government”, signalling she is ready to defy the new Prime Minister less than a week after he took office.
Her comments will be seen as further increasing tensions between the pair after Mr Johnson sacked David Mundell, a close ally of Ms Davidson’s, as Scottish Secretary.
In a column for the Mail on Sunday, the Scottish Tory leader wrote: “I believe the best thing for Britain, given our decision to leave the EU, is to take the course of action the new Prime Minister built his leadership pitch on - to leave on October 31 with a deal.
“There are huge challenges in changing that deal but I hope beyond measure the new Prime Minister is successful in getting an agreement with the EU so he can go back to the House of Commons and get the majority backing he needs. He has my full support in those efforts.”
Ms Davidson continued: “Where I differ with the UK Government is on the question of a No Deal Brexit. When I was debating against the pro-Brexit side in 2016, I don't remember anybody saying we should crash out of the EU with no arrangements in place to help maintain the vital trade that flows uninterrupted between Britain and the European Union.
“I don't think the Government should pursue a No Deal Brexit and, if it comes to it, I won't support it. I wrote to tell the former prime minister Theresa May that last year and I confirmed my position to her successor when I spoke to him last week.
“As leader of the party in Scotland, my position exists independently of government. I don't have to sign a No Deal pledge to continue to serve.”
The Scottish Tory leader rejected SNP claims that a no-deal Brexit would boost the case for independence, saying: “I doubt most Scots will be buying it.”
But she added: “I will not be backward in challenging Mr Johnson's Government where I think they are getting it wrong - and Boris is more than welcome to do the same to me when he thinks I'm wrong too.”
Ms Davidson also addressed fresh calls from Conservative commentators in Scotland for the party to consider breaking away from the UK Tories.
“Politics is about more than personalities. It's about using the power of government to deliver for the people of our country - and it is a small person indeed who forgets that,” Ms Davidson said.
“That's why I've been so irked this week by the rash of stories from political commentators floating the idea of a separate Scottish Conservative Party. I ran against that idea when I asked the party's members to elect me leader. I have been consistent in my opposition to it… my message is simple: not on my watch.”