In their opening statements, the leaders focused on the country's recovery from coronavirus.
SNP leader Nicola Sturgeon said: "Covid is not over yet. We need an experienced hand at the wheel."
She promised "bold policies to drive our recovery" as she told voters: "These are serious times, and they demand serious leadership."
Ms Sturgeon added that when the coronavirus crisis has passed, people should have a "choice on independence".
Ms Sturgeon said this was needed "so that decisions about our future lie here in Scotland, not with Boris Johnson at Westminster."
Quizzed over the SNP Government’s plans for independence, Ms Sturgeon stressed she had not put an independence bill through the Parliament, but had published a draft.
The First Minister said: "I'll leave other people to judge if my focus has been on the pandemic or not over the past year. People have seen me literally every single day lead the country's fight against Covid and I have literally spent almost every waking moment doing that.
"I will continue to do that for every single day that is required out of that crisis, because it is not over yet.
"I've spent today not on the campaign trail, but in the Scottish Government headquarters talking over with my clinical advisors, making sure we're continuing to try to take all of the right decisions."
Ms Sturgeon added: "Recovery is not a neutral thing. So long as so many of the decisions lies in the hands of Boris Johnson and Westminster – that often the people of Scotland haven't voted for, then the danger is we take the wrong decisions and go in the wrong direction just as we've been dragged out of the EU against our will."
Ms Sturgeon confirmed she would want a second vote on Scottish independence to take place in the first half of the next five-year Holyrood term “assuming the crisis has passed”.
Lorna Slater of the Scottish Greens said her party would commit to a referendum taking place in the next Holyrood term in its manifesto.
She said: “Around the room we hear people who are in favour of the union not actually arguing for the union, but instead arguing that the people of Scotland shouldn’t have the right to choose.”
She added: “The Scottish Greens would support a referendum in this term of parliament because we think decisions about Scotland should be made by the Scottish people.”
But Scottish Tory leader Douglas Ross highlighted the coronavirus vaccination programme as being one of the strengths of the United Kingdom.
With more than half of all Scottish adults having had their first dose of the vaccination, he said: “That’s the union working, the United Kingdom getting the vaccines that are delivered by our NHS staff, our British armed forces and volunteers. That’s the union working for people right now.”
Mr Ross insisted: "We can't have a recovery and a referendum."
The Tory MP, who is bidding to return to the Scottish Parliament, said the focus must be on "rebuilding Scotland".
He hit out at the SNP, accusing them of wanting to "take us through another divisive independence referendum".
Mr Ross said: "The Scottish Conservatives want to stop them. The future of our country is at stake."
Scottish Labour leader Anas Sarwar said he wanted to "focus on what unites us as a country, not what divides us".
He told the audience on the BBC Scotland debate: "This year has been the hardest of our lifetime. That's why this election must be about you, your family and our national recovery. Not egos, settling scores, or going back to the old arguments."
He pledged: ""Alongside defeating the virus, I am determined to restart our economy and create jobs, to restore our children's education and look after their mental health, and renew our NHS so that it never again has to choose between treating a virus or treating cancer."
Scottish Liberal Democrat leader Willie Rennie told the audience: "After the dreadful year we have endured, I want to spend every second, every moment of the next five years of the Parliament focusing on putting recovery first.
"That means cutting mental health waits, it means bounce back support for pupils in school, it means creating jobs for people desperate for work and it means taking action on the climate."
He insisted: "This is not the moment for another referendum. We need to put the division behind us and bring the country together."
Ms Slater, meanwhile, said the coronavirus pandemic had showed the economy had been based on low wages and insecure work.
"We must not go back to this broken system," she insisted.
She also called for action on climate change, saying: "Science tells us we have less than ten years before the climate breakdown goes past the point of no return. The time to act is now."
In the wake of announcing a 4 per cent pay off for NHS staff in Scotland, Ms Sturgeon said that five years ago, she committed to investing £500 million into the NHS over the life of the Parliament.
The First Minister said: "We've now done over three times that, not including the Covid investment. That's a sign of the way we were investing, reforming, integrating health and social care to start to bring down waiting times.
"Covid stuck and has had a devastating impact on the ability of our NHS.
"It has performed magnificently, but to deal with non-Covid cases. We are right now working on the plans to bring to bare temporary operating facilities, mobile units, to quickly bring down the backlog.
"Right now we have six permanent elective centres planned and there will be three in operation by the end of May.
"For me, this is not just about plans for an election, this is work that is under way as we speak."
Mr Sarwar said due to the backlog in NHS Scotland, a woman from Glasgow had been told she could not receive cancer treatment in Scotland.
The Scottish Labour leader said: "Just this week, I spoke to a family of Mary.
"She'd been diagnosed with ovarian cancer and been told by the NHS in Scotland that due to the backlog of Covid, they are not treating recurring cancers, and would only be treating first time cancers.
"Meaning that she will not be getting her treatment in Scotland.
"She has been forced to travel south in order to get that operation."
When asked to make a pledge to swiftly tackle any abusive behaviour going on throughout the election, taking place in the party's name, Mr Sarwar said "unequivocally yes".
He continued: "We can't pick and choose on these issues. I know from the women on the panel, from my own experience as an ethnic minority, we can't pick and choose.
"It doesn't matter where it comes from or who it is directed towards. Whether they're on our side or a different side, we have a duty to condemn those perpetrators and show solidarity with the victims.
"That's a cast-iron commitment from me."
Ms Sturgeon said she would speak out against abuse "whenever it needs to be called out".
She said: "The experience of the pandemic in the last year has changed my perspective on some of this. Let's rise to the occasion.
"Let's all, not just in our rhetoric but how we behave, try to rise to the occasion of having civilised discourse. There is nothing wrong in a democracy with passionately disagreeing, that is the essence of democracy.
"But let's do it in a civilised and respectful way."