Mr Sunak and his rival Liz Truss will attempt to win over Scottish party members during a hustings in Perth tomorrow evening.
In a statement over the weekend, Ms Truss, the Foreign Secretary, pledged that if she succeeds in becoming prime minister, she will also take on the role of minister for the Union – a position created and held by Boris Johnson.
She insisted she would govern for the whole UK “family” if she gains the keys to No 10.
But a spokesman for Mr Sunak’s campaign repeated his argument that he is “the only candidate who can defeat Labour and stop the SNP from getting into power through some backroom deal”.
The spokesman said: “For two years as chancellor Rishi broke the UK Government orthodoxy of devolve and forget, investing millions of pounds directly into local communities across Scotland.
“As prime minister he wants to double down on this, leading the most active UK Government in Scotland for decades.
“He won’t bury his head in the sand and ignore Nicola Sturgeon and the SNP – he will take them on and beat them working alongside our fantastic Scottish Conservative colleagues.”
Ms Truss previously sparked controversy by denouncing First Minister Nicola Sturgeon as an “attention seeker” who is best ignored.
Her comments were seized on by the SNP leader who said it showed Ms Truss would ignore Scotland if she wins the race for the Tory crown in a ballot among party activists.
Ms Truss, who remains the clear favourite to succeed Mr Johnson, said: “Having grown up in Paisley before going to a comprehensive school in Leeds, I consider myself a child of the Union. When I say I will deliver for our country, I mean all of it.
“My government would put the Union at the heart of everything it does and ensure that all corners of our country are rightly championed at the very top of government.
“For too long, people in parts of our United Kingdom have been let down by their devolved administrations playing political games instead of focusing on their priorities. If elected prime minister, I will deliver for our whole country.
“We are not four separate nations in an agreement of convenience, as some would have us believe. We are one great country which shares a history and institutions, but also family and friends, memories and values.
“I would ensure that our entire family continues to get the attention, support, and investment that it deserves.”
The Foreign Secretary accused the SNP of being preoccupied with the issue of independence when, she said, they should be focused on averting a recession.
The SNP accused Ms Truss of having a “total disregard” for Scotland.
The party’s deputy Westminster leader Kirsten Oswald said: “Instead of rhyming off pointless, generic rhetoric about the UK being ‘one great country’, Liz Truss must listen to the people of Scotland who voted overwhelmingly in favour of another independence referendum last year.
“The longer she denies reality, the stronger our case becomes.
“Be in no doubt, though: whoever does become the next prime minister, Scotland’s voice will be heard.”