Protesters shouted at the BBC’s James Cook as they demonstrated outside the Conservative hustings in Perth on Tuesday.
Nicola Sturgeon has labelled independence campaigners’ abuse of a journalist as “disgraceful”.
On Wednesday, Scotland’s First Minister hit out at the independence backers who abused him.
“Hurling abuse at journalists is never acceptable,” the SNP politician tweeted.
“Their job is vital to our democracy and it is important to report and scrutinise, not support any viewpoint.
“James Cook is a journalist of the highest quality and a total pro – the behaviour he was subjected to last night was disgraceful.”
Speaking to journalists on Wednesday, the First Minister said she would “condemn any abusive behaviour”.
“I’m not responsible for it, I wasn’t in Perth last night,” she added.
“That wasn’t being done in my name – as far as I’m aware it wasn’t SNP members doing that.
“If SNP members behave in that way, appropriate action will be taken.”
She added: “I want to live in a democracy where we have these debates and settle them democratically, rather than be denied the opportunity to settle them democratically.”
She went on to say she hoped that leaders in other parties would be “equally quick to call out abuse when it is directed at people like me or my colleagues in the SNP or the independence movement”.
“All politicians who care about democracy should call out this behaviour, whether it’s on their side or on the other side,” she said.
“It’s very easy to call out behaviour like this when it’s your opponents that you’re calling out – it’s harder to do when it’s people professing to be on your own side.”
When asked if SNP members should be suspended if they were found to be at the protest, the First Minister said she would not be drawn on hypotheticals.
Meanwhile, Scottish Government minister Patrick Harvie said he supported the right to peacefully protest, but added that it had to be “peaceful and respectful”.
During the video, which was filmed by protesters, Mr Cook was asked how long he had been in Scotland.
“I’ve been in Scotland my whole life,” he told the woman, who was asking about the Claim of Right, a document which dates back to 1689.
“I’m not going to be starting asking you how long you’ve been in Scotland, I think it’s a bit of a rude question.”
After yells continued from the crowd, Mr Cook said: “It’s a waste of time. I’m very much trying to have a civilised conversation with you, in our nation, which we share, but I can’t have a civilised conversation because this gentleman calls me ‘traitor’ and ‘scum’ and screams me down.”
Anas Sarwar, leader of Scottish Labour, said Mr Cook showed “incredible decency and patience” but that “no one should face this abuse”.
“Right we condemn it, but we can’t pretend our politics is separate,” the MSP tweeted.
“Let’s disagree, but always remember that Scotland belongs to us all.”
A spokesman for the BBC said: “James Cook is an exceptional correspondent and showed professionalism throughout the incident.
“It is never acceptable for journalists to suffer abuse of any nature while doing their job.”
At the protest, there were also reports of abuse being hurled at Tory members as they walked in, as well as eggs being thrown.
Scottish Tory leader Douglas Ross tweeted: “Nobody should be subjected to the abuse that happened outside @ScotTories hustings last night. It doesn’t matter if you’re a BBC reporter or a party member – you shouldn’t have to put up with nasty insults and threats. The disgusting conduct of nationalist supporters must stop.”
Scottish Conservative Party chairman Craig Hoy said: “The abuse and intimidation directed at both journalists and party members at yesterday’s hustings in Perth was completely unacceptable.
“Of course, everyone is entitled to peacefully protest and make their voice heard against politicians they disagree with – that’s the essence of democracy – but, not for the first time, a mob of extremist nationalists crossed a line.
“It’s shameful that journalists doing their job and ordinary party members, some of them elderly, had to run a gauntlet of hate just to get into the venue, including having eggs thrown at them and being spat at.”
Chief Superintendent Phil Davison said there an “appropriate policing plan was in place to maintain public safety and minimise disruption”.
“Police Scotland is a rights-based organisation that puts our values of integrity, fairness, respect and a commitment to upholding human rights at the heart of everything we do,” Mr Davidson said.
“We have a duty under the European Convention on Human Rights to protect the rights of people who wish to peacefully protest or counter protest balanced against the rights of the wider community.”
No arrests were made, the force said.