- Video report by ITV News Political Correspondent Libby Wiener
Mr Johnson pledged to fight for the union "with every breath in my body" but failed to definitively rule out granting Nicola Sturgeon the power to hold a second independence referendum.
Jeremy Hunt, the rival candidate bidding to succeed Theresa May as prime minister, insisted he would say a "polite" no to any request from the Scottish First Minister.
On a visit to the shipyard BAE Systems earlier on Friday, Mr Johnson dodged questions over comments he made in the past accusing Scotland of "free-riding on English taxpayers", insisting he wanted to see "that Scotland is properly funded and making sure also that we celebrate the things that the Union brings to Scotland."
He said: "I think it's very important to keep our fantastic union together. I'm a massive defender and supporter of the union and if I'm lucky enough to be elected I will be doing everything in my power to cement the union."
The Brexiteer repeated his arguments that taking the UK out of the EU - something most Scots voted against - could strengthen the union. He said: "The union must come first and I believe also, as it happens, that a good, sensible, pragmatic Brexit will strengthen the union."
He described himself as being a "passionate unionist", telling reporters: "I will defend it, fight for it with every fibre in my being every breath in my body."
At the hustings in Perth, Mr Johnson described the Scottish 2014 referendum as a "decisive win".
"We did it then, people voted then, they were assured that their votes were decisive, they were told this was a once in a generation thing and I think we should stick to that promise."
Mr Johnson was asked whether he was bothered Scottish Tory leader Ruth Davidson had backed Mr Hunt to be the next prime minister amid reports that Scottish Conservative MPs have mounted a campaign called "Operation Arse" to thwart his leadership ambitions, he replied "not in the slightest".
He said he had the support of "more than half the parliamentary party" at Westminster.
"So when it comes to the crucial work ahead of us of getting Brexit done, of building a coalition across our party, uniting everybody, I think we are most of the way there," he said.
Mr Hunt also vowed to keep the union together, saying he would refuse to allow a second Scottish independence referendum.
"As prime minister of the UK I will never allow our union to be broken up.
"And if the First Minister of Scotland asks me for a second independence referendum, I will muster up my British politeness and I will say 'no'."
He said he would "defend our precious union with every drop of blood I have".
Mr Hunt said he would mitigate the impact of a no-deal Brexit in response to claims it could threaten the union.
"We should always be alive to the risks to the union but also confident about its great, great future," he said.
"If we get things wrong then of course those risks increase."
He added: "That's why, if we end up with a no-deal Brexit we have got to take every possible measure to prepare and support businesses in Scotland and other parts of the UK."
The foreign secretary also hit out at the Scottish Government, saying ministers in Edinburgh must do more to prepare for the possibility of a no-deal Brexit.
He claimed the current arrangements were "very disappointing", saying: "All of us have to do more but to date as I've been watching the no-deal preparations I would like to see more focus on that from Nicola Sturgeon.
"(The Scottish Government) have been very disappointing in their preparations of a no-deal Brexit, which none of us want, but any responsible Government or authority in the United Kingdom should be taking seriously because there is that risk."
He insisted it was "not the time" to detail what steps the Scottish Government should be taking but added: "I think they know, and we know, the areas where more can be done."
Addressing the audience at the hustings in Perth Concert Hall, Mr Hunt attacked the SNP as "the most bullying, divisive, duplicitous, anti-business government that Scotland has ever seen".
Earlier, Mr Johnson denied allegations that Downing Street attempted to restrict intelligence to him while he was foreign secretary for fear of him being indiscrete with sensitive material.
The Conservative leadership hopeful said he "certainly" knew nothing about the claims, adding "it's not something I would comment on even if it was true."
Pressed on claims Mrs May ordered withholding some information from him, Mr Johnson said: "I am sure that the Prime Minister would not comment on intelligence matters either so I am extremely dubious about the provenance of this story."