Ruth Davidson has said she will back Boris Johnson as Prime Minister - but will not give her support to a no-deal Brexit.
The Scottish Conservative leader also insisted that her position in the Scottish Parliament exists independently of Westminster and that she does not have to sign any no-deal pledge to continue to serve.
In a major reshuffle at Number 10 last week Mr Johnson installed a number of Brexiteers in key Cabinet posts as more than half of Mrs May's top team had quit or been sacked, including Secretary of State for Scotland David Mundell.
Writing in the Mail On Sunday, Ms Davidson said: "I hope beyond measure that the new Prime Minister is successful in getting an agreement with the EU so that he can go back to the House of Commons and get the majority backing he needs. He has my full support in those efforts.
"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 UK Government should pursue a no-deal Brexit, and if it comes to it, I won't support it.
"I wrote to tell Theresa May that last year and I confirmed my position to her successor 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."
Ms Davidson also rejected any suggestions of the party in Scotland splitting from the UK, with the idea having previously been mooted around the time of the last Scottish Tory leadership race.