Nicola Sturgeon is being pressed to say if she is planning to mount a legal challenge as part of her "war of attrition over independence".
Scottish Liberal Democrat leader Willie Rennie is demanding answers from the First Minister after she told an audience in the US the part of the Scotland Act which reserved powers over the constitution to Westminster had never been tested in court.
In a question-and-answer session following a speech at Stanford University, Ms Sturgeon also said that it was "quite a vague term".
Read more: Ex-Scottish minister says another independence vote would affect 'day job’
She is in a stand-off with Theresa May over the prospect of a second ballot on independence, with the Prime Minister having insisted "now is not the time" for a fresh vote to be held.
Mr Rennie has now written to the SNP leader, asking her to provide "clarity on exactly what you are planning to do and what you meant in your remarks to the American audience".
He told the First Minister: "I am alarmed that you are considering testing the reserved power on the UK constitution in the courts."
He added: "When you stated the constitution is reserved to the UK Government I assume you meant UK Parliament.
"Is it your intention to test the reservation of the constitution of the United Kingdom to the United Kingdom Parliament? When would you be planning to test this in the court? What is the basis in law for this? Have you already instructed the Lord Advocate to prepare for this? Have you estimated the cost of taking such action?
"I am sure that you will understand that a majority of people in Scotland now believe that you are being wholly distracted by the issue of independence and this most recent threat is yet another example of that.
"I would urge you to focus on the enormous challenges that our country faces rather than continuing this war of attrition over independence."
Lord Mandelson: Theresa May must stand up to Tory 'wild men' on Brexit talks
In her speech at Stanford University, the First Minister told the audience she is seeking "legal consent from the Westminster government to legislate for an independence referendum, which at the moment they're saying they're not willing to give".
She stated: "That is not a sustainable position, frankly, for the UK Government to take, it is a bit of a holding position just now.
"There will be another referendum on Scottish independence, of that I am fairly certain."
The Scottish Government insists a second referendum is needed to give Scots a choice between Brexit and independence, with Ms Sturgeon having proposed such a vote be held between autumn 2018 and spring 2019, when the terms of the UK's exit deal from the European Union are known.
Read more: Ex-Scottish minister says another independence vote would affect 'day job’
While the decision to leave the EU was backed by a majority of voters in the 2016 referendum, 62% of Scots who took part opted for remain.
A spokesman for the First Minister said: "There is a cast-iron democratic mandate for giving the people of Scotland a choice on their future - and the referendum we are intent on delivering is the same kind as that which took place in 2014.
"We agree with the Prime Minister that now is not the time for a vote, but if the UK Government's intention is to try and indefinitely block a referendum that would be utterly undemocratic and unsustainable.
"People across Scotland already disagree with that stance and public opinion is only likely to turn even more sharply against the PM the longer she tries to stick to that position."
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