Liz Truss insisted she would ensure the union went from strength to strength “now and forever” while her rival Rishi Sunak said he could not "imagine the circumstances” in which he would agree to a second independence referendum.
It came as both candidates faced a grilling over the cost-of-living crisis as they addressed the only Scottish hustings of the Conservative leadership contest in Perth.
Earlier, around 300 protesters jeered and booed from behind metal barriers as party members entered Perth Concert Hall, with one prominent banner reading “Tory scum out”. Many of the protesters waved saltires and Yes flags.
As The Scotsman arrived, eggs were thrown towards a queue of Tory members that included older men and women and a wheelchair user.
SNP MP David Linden condemned the behaviour, writing on Twitter: “If any one of them is found to be an SNP member, then they should be chucked out immediately.”
During the hustings, which was attended by around 1,000 Tory members and chaired by STV’s political editor Colin Mackay, both Ms Truss and Mr Sunak repeatedly attacked the SNP’s record in Government.
Mr Sunak said public spending on the NHS in Scotland is growing at a far slower rate than in England.
He said: “Then look at the rest of the public sector, education, justice, local government. [Ms Sturgeon’s] imposed austerity on all those parts of public services.
“I even put an income tax cut in and gave the Scottish Government money to pass that on. They chose not to do that.
“You might scratch your head and say ‘hang on, where is all that money going then? We found out – the welfare budget in Scotland is increasing by 50 per cent over the next five years.”
He said it was “barmy” for any government to focus on a second referendum during a cost-of-living crisis.
Mr Sunak promised he would “not be shy” about calling out the SNP’s record in Holyrood if he becomes the next prime minister.
He said the cost-of-living crisis should be the focus of both the devolved and Westminster governments, adding: “Politicians should be relentlessly focused on addressing that, and I say that to Nicola Sturgeon, that is the priority, not another divisive, unnecessary constitutional referendum.”
In a reference to previous comments by Ms Truss, he added: "I don’t want to just ignore Nicola Sturgeon. I want to take her on and beat her.”
Mr Sunak said the SNP could not be trusted to deliver economic growth as they “can’t even get the ferries to work”.
Earlier, Ms Truss told the audience she would not let the “family” of nations in the UK be split up.
She said: “I consider myself a child of the union and to me we’re not just neighbours, we’re family. I will never ever let our family be split up.”
She added: “I will make sure that, now and forever, our fantastic union goes from strength to strength to strength.”
Ms Truss said Scotland is being “let down by Nicola Sturgeon and the SNP Government”.
She said: “They’ve been pursuing an agenda of separatism rather than dealing with issues that they created in the Scottish education system, in the NHS and in the transport system”.
“I know the people of Scotland deserve better, and they want better.”
The Foreign Secretary said the number of defence contracts being given to Scottish firms would increase if she becomes prime minister.
Elsewhere, Mr Sunak said the cost-of-living crisis is the most important issue facing the country, but ruled out freezing the energy price cap to help struggling households with growing costs, as the Labour Party has urged.
Ms Truss refused to say what support other than pausing the green energy levy she would offer people to limit the impact of energy bill rises.
She said she did not want to pre-empt a budget given by a chancellor she would appoint.
On independence, she told the hustings: “If I am elected as prime minister, I will not allow another independence referendum.”
Mr Sunak was also pressed on whether he would allow a referendum. He said: “I can’t imagine the circumstances in which I would.
“We live in a union which is of course there by consent and by democracy and I accept that, but I just don’t think that anybody thinks that now or any time in the near future is remotely the time to focus on this.”
Both candidates toured the north-east of Scotland ahead of the hustings in Perth, with Ms Truss visiting the BenRiach distillery near Elgin before heading to an event in Aberdeen.
Mr Sunak met the Scottish Fishermen’s Federation in Stonehaven and then travelled to Cluny Castle and across to Aberdeen.
Kirsten Oswald, the SNP’s deputy Westminster leader, said the hustings event was “depressing watching for Scots”.
She said: “It seems both Rishi Sunak and Liz Truss have very short memories - and it became even clearer that neither have a clue what ordinary folk are facing during this cost-of-living crisis, nor do they have a plan to support them.
“That is because they have spent their time in the Tory government making the rich richer and the poor poorer.
"Sunak wants to take from the poor to give to the rich, and Truss thinks the solution to all problems is for British workers just to "graft" more. The options for the next UK Prime Minister are truly grim.
“The pair repeatedly attempted to tell us tonight what Scotland wants. Scotland has made it clear what it does and doesn’t want by repeatedly rejecting the Tories at the polls and repeatedly voting for independence supporting parties.
“Scotland hasn’t voted for the Tories since the 1950s yet we keep getting saddled with Tory governments and Prime Ministers.
"We were told in 2014 that Scotland’s place in the EU would only be safe if we rejected independence – that was a lie.
"It’s time Scotland had a say on its future – and it’s clear that whoever wins this gruesome Tory contest will only increase support for independence.”
Scottish Liberal Democrat deputy leader Wendy Chamberlain said: "I had to switch off after fifteen minutes.
“Over the course of this campaign neither candidate has made any effort to talk about Scotland and devolution beyond superficial platitudes that only play to their narrow Tory party member electorate.
“Scotland needs a Prime Minister who is prepared to get serious about the cost-of-living crisis and stop playing into the hands of the nationalists. We will never get that with the out-of-touch Conservative party. A general election cannot come quickly enough.”