Boris Johnson has promised to do “anything” in his power to stop the UK breaking up if he becomes prime minister.
The Conservative leadership candidate said the next occupant of 10 Downing Street should be “minister for the union” as well as prime minister.
Meanwhile his rival, Foreign Secretary Jeremy Hunt, confirmed he would be willing to leave the EU without a deal.
He had previously said preserving the union was more important than Brexit.
The SNP said both candidates were ignoring calls from their Scottish colleagues to rule out a no-deal Brexit “or accept that Scotland will choose another path”.
Writing in the Mail on Sunday, Boris Johnson said he was a “passionate believer” in the union.
He said the next prime minister should be “minister for the union” – something he described as a “cost-free but symbolically significant important addition to the office I seek”.
And he suggested that there should be a unit at Number 10 to “sense-test and stress-test” every policy for the results it would have on the union.
“We should actively campaign for a public understanding of the benefits of the union, economic and strategic, for the people and its component nations,” Mr Johnson added.
“There are still passionate voices – especially in Scotland – that are campaigning night and day to break our union up, to diminish our country.
“We cannot just leave the field to them, a refuse to engage in the argument.”
The former foreign secretary also claimed that delivering a “sensible” Brexit would make it harder for the SNP to argue for independence.
His comments came a week after an opinion poll suggested there would be majority support in Scotland for independence if Mr Johnson became prime minister.
And earlier this month a YouGov poll a majority of Conservative party members said they would prefer Brexit to go ahead even if it caused Scottish independence.
On BBC One’s The Andrew Marr Show, Mr Hunt admitted that leaving the EU without a deal would be unpopular in Scotland.
His cabinet colleague, Scotland Secretary David Mundell, has said that a no-deal Brexit could “threaten the continuance of the United Kingdom”.
But Mr Hunt said that – if it came to it – he could deliver a successful no deal Brexit and strengthen the union with Scotland.
“There are risks,” the foreign secretary conceded. “You think about what someone like Nicola Sturgeon would do politically if we had a no deal situation and we would have to get through that, and that is why a no-deal Brexit is not my first choice. “
He said it was not question of choosing Brexit or the union.
“If you send to Brussels someone who can negotiate a deal that can get through Parliament, then you won’t have a no-deal situation, and then you reduce those risks,” he added.
“But I’m also very clear that we are going to leave the European Union come what may and I will deliver that. If that happens, I will do it in a way that protects the union because it’s absolutely vital that we do.”
The SNP dismissed Mr Johnson’s plan for a “minister for the union” as a “meaningless gimmick”.
MSP Tom Arthur added: “Jeremy Hunt has made clear that he’s more than willing to push through a disastrous no-deal Brexit despite knowing the disproportionate damage this will bring to jobs, businesses and households incomes in Scotland.
“Both the candidates to become the next Tory leader have publicly ignored calls from their Scottish colleagues to rule out a no-deal or accept that Scotland will choose another path.
The 160,000 Conservative party members will begin voting for their new leader next week and Theresa May’s successor is expected to be announced on 23 July.