Ms Badenoch has surprised some with her success in the contest, winning the votes of 49 fellow Tory MPs in the most recent ballot.
Writing in the Times, Ms Badenoch said Scotland was “integral” to the success of the wider UK, adding: “As prime minister I would champion Scotland’s interests, its place in our UK and its amazing potential.”
The former equalities minister also said she would work with the Scottish Government.
“If I become prime minister, I will be focusing on strengthening local communities and businesses across Scotland,” she wrote.
“I will also work with the Scottish Government on issues where we have common interests, the success of the vaccine rollout and the Homes for Ukraine programme showed the UK government delivering for Scotland in partnership with Holyrood.
“But I won’t be afraid to call out the SNP when they let Scotland down.”
The candidate said the Scottish Government had delivered “lower educational standards”, presided over spiralling cancer treatment waiting times and “screwed up” the country’s transport system.
“Scotland deserves so much better,” she added.
“It needs real change.
“A move away from the politics of division towards a new narrative of national unity.
“The SNP thrive on generating grievances and setting people against each other.
“They blame England for injustices rather than bringing Scots of every background together in a common endeavour.”
But both Ms Badenoch and Foreign Affairs Committee chairman Tom Tugendhat are vying to remain in the contest as the bottom two heading into the vote on Monday.