Nicola Sturgeon believes it is inevitable that the killing of Jo Cox will have an impact on the EU referendum and suggests that voters will be increasingly disgusted at the “poisonous” nature of the campaign after the politician’s death.

Speaking to the Guardian on Monday, as the Westminster parliament paid tribute to the 41-year-old Labour MP who was fatally attacked in her West Yorkshire constituency last Thursday, Sturgeon said: “I think it inevitably will [affect voting decisions]. It’s too early to say whether it will have a direct impact on the result. I think there was a bit of disgust setting in on Thursday morning about the Farage poster. I started to detect a sense of ‘if you’re voting leave, are you associating yourself with that?’.

“Obviously nobody knows whether the debate around the referendum had anything to do with what happened to Jo, but the sense that the debate had become a little bit poisonous and a little bit intolerant and focused on fear of foreigners as opposed to legitimate debate about immigration, I suspect what happened will have intensified those feelings.”

Scotland’s first minister also said that the media’s treatment of Cox’s death risked ignoring the wider politics around the attack, suggesting that it would have been very different had the alleged perpetrator been a Muslim. “The [media] treatment of this event has been very different from the treatment of other attacks that have been equally horrific. I do feel that if the person arrested for this had been Muslim, for example, the treatment would have been very different.”

Describing herself as disappointed by how focused the referendum campaign has become on immigration, the SNP leader accused leading Brexit campaigners of “exploiting and twisting” people’s fears. “The leadership of the leave campaign – and I emphasise leadership because there are lots of people who will be voting leave for reasons that I don’t agree with but nonetheless are legitimate reasons and don’t deserve to be dismissed by calling them racist and intolerant – what the leadership have done, and I’m not just talking about Nigel Farage, but Boris Johnson and others, is to allow themselves to be associated with this view that pressure on our public services is the fault of immigrants, immigrants are the fault of the EU and therefore the answer is to close our borders and pull up the drawbridge. It has been really, really distasteful.

“[It’s] not that I think that people’s concerns should be ignored, but the leave campaign has exploited and tried to twist people’s fears around immigration into something that is really distasteful.” All politicians should draw a lesson from the referendum that there was a “need to change the tone and the narrative around immigration”, she said.

Asked whether there were plans in place to initiate the process for a second Scottish independence referendum should there be a Brexit victory on Thursday, in which the majority of Scots vote to remain but are dragged out of the EU by other parts of the UK, Sturgeon said: “Our manifesto was very clear that the Scottish parliament should in these circumstances have the right to propose another referendum. Even if we don’t take the decision straightaway that it’s definitely happening in a particular timescale, we’ll have to start doing certain things to keep that option open. It takes time to legislate for a referendum. So it’s going to be really important to make sure that every option that is available to Scotland to protect our position is kept open.”

She insisted, however, that she genuinely hoped not to find herself in such a position. “I want there to be another independence referendum at some stage, I want Scotland to be independent, but I wouldn’t choose to have it happen because England votes to come out of the EU.”

Reflecting on the longer term impact of Cox’s death, Sturgeon suggested that politicians needed to counter their critics while leading by example when it came to changing the tone of debate. “Maybe its time for politicians to fight back a little bit in terms of this notion that politicians are all in it for themselves, we’re all the same, we’re not driven by sincere motives. Because the fact of the matter is the vast majority are. Most politicians come into politics because they want to make a difference, we just have different ideas how to do it.

“It’s very much the currency of discourse on social media where political disagreements very quickly become very personalised. It would be naive to think that this tragedy is suddenly going to change all of that, but maybe the next time someone is about to compose a tweet that hurls personal abuse they could think twice. Politicians, while we can’t control the tone of debate on social media completely, we can lead by example.”

She cautioned, however, against forfeiting passion in pursuit of a gentler discourse. “I didn’t know Jo at all, but everything that I’ve read about her in the past few days leads me to believe that the last thing she would want would be for us to stop being really passionate about political debate. When people talk about changing the style of politics it’s important we don’t have that mean politics becomes anodyne.”