Douglas Ross had issued the challenge to Nicola Sturgeon to face him in a debate on the demands from the SNP for a second referendum in a speech earlier on Monday.
But Ms Sturgeon said she had a “real job to do” and was focused on guiding Scotland through the Covid-19 pandemic.
Speaking at her daily coronavirus briefing, the First Minister said she was "confused” by the request.
Ms Sturgeon said: “I’m a little bit confused. The leader of the Conservatives appears on the one hand to not want me to talk about politics and focus on the pandemic, which is exactly what I have been doing and will continue to do, my only focus right now is on the pandemic.
"On the other hand, he is challenging me to a debate on politics. I think he might be in danger of looking a bit silly.
"I’ll leave others to play games or politics. I have got a real job to do and people can decide themselves whether I am doing it well or not, but I am absolutely 100 per cent focused on leading this country through a pandemic.
“That’s what I’ve done since this time last year and it’s what I’m going to continue to do for absolutely as long as necessary.”
Any potential debate would need the agreement of both leaders and would likely be televised, but the challenge was labelled “patently ridiculous and hypocritical” by the SNP’s deputy leader Keith Brown.
Mr Ross had said: “If she believes that this referendum plan is an essential part of Scotland’s economic recovery from coronavirus, then she should explain it to the Scottish people.
“So let’s not wait for the election.
“Nicola Sturgeon, SNP leader, let’s you and I debate our respective positions right now."
Stewart McDonald, the SNP MP for Glasgow South, criticised Mr Ross’ stance, tweeting: “Few will take seriously any claims about work ethic from a man who is a part-time MP, some-time football linesman and is seeking another job as an MSP, all at the same time.
"That’s before we get to the absurdity of the claim itself.”