His comments were made as the SNP prepares to take up its fourth term as the Scottish Government, with an overall majority on a knife edge.
SNP leader Sturgeon vowed to pursue a second referendum if her party makes up the next government, with plans for a follow-up border poll.
Boris Johnson told the Daily Telegraph that another referendum would be “irresponsible and reckless” in the “current context” as Britain emerges from the coronavirus crisis.
This outlook was reiterated by the UK Environment Secretary, George Eustice, who told Times Radio that a second Scotttish referendum would be “irresponsible” and “a complete distraction”, at a time when governments should be focusing on recovering from the Covid pandemic.
He added that the previous referendum, held in 2014, “settled the issue”.
Meanwhile, Sturgeon told ITV news that a fourth term in government for the SNP was an “extraordinary achievement” and said Johnson would need to go to the Supreme Court if he wished to overturn a Scottish parliament vote to hold a referendum.
She said: “We would proceed with the legislation that is necessary, and that would only happen if it was passed by the Scottish Parliament.
"If he [Boris Johnson] wanted to stop that it would be the case that he would have to go to the Supreme Court to challenge it - and that would be his decision not mine.
She continued: "The absurdity of a position where a PM was going to court to overturn the democratic decision of the Scottish people? I don't think we'll get to the position."
When the legal challenge was put to Eustice on BBC Breakfast, he said he wouldn’t “get ahead of [himself]”.
SNP majority ‘on a knife edge’
Eustice said: “Look, I’m not a lawyer – lawyers will look at these things and I think it is getting ahead of ourselves.
“There is a question at the moment over whether the SNP will get a majority or not – we’ll have to wait and see until the results come through.”
The SNP’s chances of a majority are currently on a knife edge, it needs 65 seats to win an overall majority.
The SNP picked up key seats in Edinburgh Central, Ayr and East Lothian, and held on to Aberdeenshire East, which was the first result to be announced on Saturday. However, it failed to take marginal seat, Dumbarton, from Labour’s Jackie Baillie.
The pro-independence Scottish Green Party could make up a pro-indy majority in the Scottish Parliament though, as the party looks set to take several regional seats on the Scottish list. Therefore, when voting in the Scottish Parliament for a second referendum there could be a pro-independence majority.