The Tory leadership candidate promised Conservative members he would oppose the SNP with “an argument that speaks to people’s hearts” if elected as prime minister of the United Kingdom.
The commitment comes as the Chancellor, Nadhim Zahawi, will visit to Edinburgh on Wednesday to emphasise the UK Government’s commitment to energy security.
Both Mr Sunak and his opponent Liz Truss continue to face scrutiny about how they would tackle rising energy costs if elected prime minister.
On Tuesday, Mr Sunak told a leadership hustings in Birmingham that as chancellor he had started to “more actively demonstrate the benefit of the union in Scotland”.
He said: “When it comes to arguing for the union, we have to remember nationalism is very seductive, it’s a romantic idea, and we have to fight that idea with an argument that speaks to people’s hearts,” he added.
Mr Sunak had earlier warned that millions of households could face “destitution” this winter if Foreign Secretary Ms Truss wins the leadership election, and claimed her economic plans would “pour fuel on the fire” of inflation.
His campaign has sought to discredit Ms Truss’ economic credibility in recent days, questioning why her proposed emergency budget would not include an economic forecast from the independent Office for Budget Responsibility.
But his successor as Chancellor Mr Zahawi, who is backing Ms Truss, claimed that she “understands the economics of growth”.
On Wednesday, Mr Zahawi will reaffirm the UK Government’s commitment to help Scots with the rising cost of living as he visits Edinburgh.
The Chancellor said he knew “families across Scotland are feeling anxious about rising costs” but added the “UK Government has stepped in to ease pressures on household budgets” as part of a £37 billion package of support.
Some 689,000 households north of the border are expected to receive a £650 cost-of-living support payment, according to the Treasury.
Ms Truss, the frontrunner in the leadership race, has pitched herself as a “child of the union”, having spent part of her childhood in Paisley in Scotland, and part in Leeds in the north of England.
She defended her tax-cutting plans against what she described as “Treasury orthodoxy”, and sought to pitch them as a new economic model to deal with living costs in the long-term.
Ms Truss told the Birmingham hustings: “This whole language of ‘unfunded’ tax cuts implies the static model, the so-called abacus economics that the Treasury orthodoxy has promoted for years, but it hasn’t worked in our economy because what we have ended up with is high tax, high spending and low growth.
“That is not a sustainable model for Britain’s future.”
She said she was “very aware that many people across Britain are struggling” with rising bills, and described cutting taxes as her “first port of call” if elected prime minister.
“The second port of call will be looking at the energy supply and making sure we are doing all we can as soon as possible,” she added.