Penny Mordaunt, trade minister in the UK Government, said she would overturn the SNP’s electoral dominance by breaking down their “yellow wall”. She also claimed the Scottish Conservatives have the potential to win power at Holyrood if she took over from Boris Johnson.
On Monday evening the Tories' 1922 committee, which sets the rules for a leadership race in the party, said the new leader would be announced on Monday 5 September.
Nominations for the PM’s successor close today and party MPs will whittle down a list of 11 contenders to two people, with the final choice made by Tory members.
Writing in the Scottish Daily Mail, Ms Mordaunt said: “In this leadership contest, you will not only hear me talk of winning power across our United Kingdom. You will also hear me talk of winning power in Scotland, as difficult as it will be to achieve.
“We must set our sights that high. We are the only party that has ever shown the strength to stand up to the SNP.
“It will be a long road to get there but we must aspire to unite the pro-UK majority and form the Scottish Government. We must be a party that seeks power everywhere in our United Kingdom.”
On indyref2, Ms Mordaunt refused to set a timescale for when another referendum could be acceptable.
She said: “I won't play Nicola Sturgeon's games. When asked about a referendum, you'll hear me answer instead about people's real priorities, such as how we can put more of your hard earned money back in your pocket. I am firmly against playing on the SNP's turf.
“Another divisive referendum at this time is the wrong priority and I won't be afraid to say so, firmly, to Nicola Sturgeon, just as I have in the House of Commons to Ian Blackford.”
Other candidates, such as Sajid Javid and Jeremy Hunt, have said they would not consider an independence referendum in Scotland for at least ten years.
The Scottish government wants to hold a vote on the issue in October next year.
Responding to the comments made by Ms Mordaunt, SNP MP Mhairi Black said: "Beyond the rhetoric, Penny Mordaunt - along with her fellow Tory leadership candidates - offer nothing but a continuation of deeply damaging Tory policies that have punished households and businesses across Scotland.
"The fact is that whoever replaces Boris Johnson, Scotland will still be saddled with a Tory government we didn't vote for imposing Brexit, austerity cuts and harmful policies against our will.
"The question for Tory candidates is whether they will respect democracy and the people of Scotland's decision to decide their own future. The Scottish Government has been given a cast-iron democratic mandate by the people to hold an independence referendum – and that is what we intend to do on 19th October 2023.”
Two of Scotland's six Conservative MPs revealed who they will be backing in the race to replace Boris Johnson as party leader and prime minster.
Borders MP John Lamont said he would vote for International Trade Minister Penny Mordaunt while West Aberdeenshire MP Andrew Bowie confirmed he would support former Chancellor Rishi Sunak.
The remaining four, including Scottish Conservative leader Douglas Ross, have yet to endorse any of the candidates.
Scottish Secretary Alister Jack, the MP for Dumfries and Galloway, has also yet to say who he will support and earlier, Mr Johnson declined to back any of the contenders.
Rishi Sunak, who quit as Johnson’s chancellor last week, will today unveil his policy platform.
He has cautioned against early tax cuts and stressed the importance of taming sky-high inflation.