Nicola Sturgeon has said Liz Truss will be a "disaster" as prime minister if she governs how she has campaigned.
Scotland's first minister said she will "try" to have a good working relationship with the Tory leadership frontrunner if she wins on Monday, as is expected.
The pair have traded barbs throughout the race for No 10, but Ms Sturgeon told Sophy Ridge on Sunday that she will give Ms Truss a chance.
She said: "It's obviously the case that Liz Truss and I don't agree on very much politically, but I'm a firm believer in giving anybody who's coming into the office of prime minister a chance to prove themselves, and I will certainly do my best to build a constructive working relationship with her."
However, she added: "If she governs how she has campaigned over the summer, she will be a disaster - not just for Scotland but for all of the UK - but let's hope that's not the case, because this is a very serious time for the UK and it needs very serious and very purposeful leadership."
When asked to expand on her view of Ms Truss's campaign, Ms Sturgeon accused her of focusing on the "niche priorities" of Tory members, such as tax cuts.
"The obsessions of a tiny, tiny number of Conservative Party members are not the right priorities for the country," she said.
Ms Sturgeon said it won't take very long to see "whether she is going to govern as a prime minister with a focus on the real priorities of the country or not", adding: "Let's hope she chooses the responsible course and stops pandering to the margins in the Conservative Party."
Ms Sturgeon also said a fear of losing a referendum on Scottish independence is not a reason to rewrite the rules of the contest, amid reports of plans from Ms Truss.
'Don't re-write rules of democracy'
The Sunday Times reported that the Tory leadership frontrunner wants to pass a new law that would bar another independence referendum until polls show 60% of Scots favour a new vote for at least a year.
Support for independence in the polls peaked at 58% during the pandemic but that figure has slid in recently.
The terms of the referendum would also be changed so at least 50% of the total electorate in Scotland had to vote in favour of Scotland's secession for the country to leave the union.
Ms Sturgeon said the reported reform would be "a changing of the basic rules of democracy that we have all abided by for our entire lifetimes and long before that".
"Just because you fear losing a democratic contest, it's not an excuse or doesn't make it acceptable to rewrite the rules of democracy," she added.
Ms Sturgeon said she had never considered Ms Truss to be a "shrinking violet" but the proposals were an attempt to "gerrymander the rules".
She said: "That is a sign of fundamental weakness and a lack of confidence in her case for the union."
Ms Sturgeon went on to insist that another referendum would not distract from the cost of living crisis, saying an independent Scotland would have more powers to help households struggling with soaring energy bills - such as setting an emergency budget and reforming the energy market.
"Actually, independence is much more necessary when we're dealing with a crisis because it gives you more levers to navigate your way through and on to a better future," she said.
The UK Supreme Court is currently considering whether another referendum is within the powers of Holyrood, with oral arguments to be heard in the case next month.
Ms Truss has previously said she would "ignore" Ms Sturgeon's desire for another referendum if she becomes prime minister, and branded her an "attention seeker".
The first minister hit back and said the foreign secretary asked her how to get into Vogue when they met briefly last year.