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SNP leader Nicola Sturgeon accused Tory counterpart Ruth Davidson of "talking so much about independence that I can't get a word in edgeways about it".
But Ms Davidson hit back by telling Ms Sturgeon: "The country said 'No' and you won't listen to them."
Scottish Labour leader Kezia Dugdale said people "want to move on" from the referendum.
The televised debate, which was hosted by the BBC's Sarah Smith in front of a live audience, also featured Willie Rennie of the Scottish Liberal Democrats, Scottish Green Party co-convener Patrick Harvie and UKIP's David Coburn.
Ms Sturgeon opened the debate by arguing that only her party could protect Scotland from an "extreme Brexit".
And she said that supporting the SNP would "protect Scotland's right to make our own decisions" with regard to an independence referendum.
The first minister was followed by Ms Davidson, who told Ms Sturgeon that she should: "Fix our schools, don't split up our country. Champion our businesses, don't put a border at Berwick."
She added: "At this election we can send the SNP a message they can't ignore, and with your help we can stop them, and in so doing we can get back to the issues that really matter."
Ms Sturgeon responded by accusing the Scottish Conservative leader of using independence as a smokescreen for her party's "toxic" policies.
She said: "Ruth Davidson says I talk about nothing else, the truth is she talks so much about independence that I can't get a word in edgeways about it.
"Ruth Davidson is using independence as a smokescreen in this campaign because she knows the Tory record and Tory policies are toxic."
Ms Dugdale warned the opinion polls were suggesting that the Conservatives "will be back and they will be more destructive than ever before" after the election.
She added: "So who do you want to stand up to the Tories? Labour MPs who understand your life, because they've lived, or SNP MPs who will use every bit of Tory cruelty to exploit the case for independence."
Mr Rennie said the SNP's focus was "always independence", adding: "It took 44 days for Nicola Sturgeon to publish her Bill on another independence referendum. It took 15 months for them to write their mental health strategy.
"It took two years for us to persuade them to expand nursery education for two-year-olds and it took six years for us to persuade them about a pupil premium."
Meanwhile, Mr Harvie warned social and environmental rights, guaranteed in the EU, would be "in the hands of a hard right Tory government hell-bent on a bonfire of the regulations".
And Mr Coburn used his opening remarks to state that "UKIP is the party of Brexit. We must elect UKIP to the Commons to ensure Brexit means exit".
The debate also saw Ms Sturgeon come under fire from the politically balanced audience over the SNP's record on health and education - both of which are devolved to the Scottish Parliament.
One member said she was a nurse and had been forced to use a foodbank.
She said that colleagues were considering leaving nursing, adding: "You have no idea how demoralising it is to work in the NHS."
Making a direct plea to the first minister, she said: "Don't come on your announced visits, come in in the middle of any day to any ward, to any A&E department and see what we're up against."
Ms Sturgeon told her "My sister works in the National Health Service, believe me she tells me exactly what she thinks about these matters."
She said the "austerity policies" of the UK government meant public sector workers had had pay rises capped at 1%.
And she stressed that the Scottish government had a policy of no compulsory redundancies in the NHS and wider public sector.
By Philip Sim, BBC Scotland political
At times it was like a Thursday session of First Minister's Questions, with the leaders of the main parties trading barbs over a faintly baffling mix of devolved and reserved policies. With the SNP defending 56 seats, it was natural that the other leaders would target Nicola Sturgeon, and
Ruth Davidson and Kezia Dugdale dominated the early stages with attacks on the SNP's record in government, although the Scottish Tory leader came under sustained pressure herself over immigration.
There were the usual bouts of participants shouting over each other, and but it was notable that Ms Sturgeon came under much more detailed scrutiny than she did during the UK-wide debate on ITV on Thursday.
The first minister is a skilled operator when it comes to this political sparring though, so she held her ground reasonably well; it was a member of the audience who landed the most notable blow on her.
The nurse in the audience who took the first minister to task will go down as the most memorable moment of the debate, and will no doubt be the element which leads tomorrow's headlines.
There were also fierce exchanges between Ms Sturgeon and Ms Davidson over immigration, with the SNP leader arguing that Conservative manifesto pledges to slash net migration to the UK would be "devastating" for Scotland's economy.
Calling for politicians to be "honest" about immigration, Ms Sturgeon continued: "When we are talking about migrants here we are talking about people working in our hospitals, people serving us in our restaurants, we are talking about our friends and our neighbours.
"The language around immigration I think is shocking. We have got a need in this country to grow our population.
"If EU migration was to be ended over the next 25 years, or even constrained, we would see our working age population fall while our pensioner-age population is due to go up by 50%. That would be an economic catastrophe."
Ms Davidson said that "no one is talking about ending" migration from the EU, and that it was important that any immigration system was "trusted" by people in order to avoid it causing social unrest.
She added: "What I want to see is Scotland to be the most attractive place so we can attract the brightest and the best. At the moment, despite having a third of the landmass of the UK, and 8.4% of the population, we only attract 4% of immigrants to this country".
Ms Sturgeon said those figures - which Ms Davidson said were from the UK government - were "not true", and instead pointed to National Records of Scotland figures which said the country attracted 7% of migrants to the UK.