The First Minister insisted she had “no plans to go to court” over Theresa May’s block on another divisive separation vote.
Critics feared she was plotting a costly legal challenge after claiming earlier this week that Westminster’s power over constitutional issues was “untested”.
Ms Sturgeon, who is on a visit to the US, had argued that the “vague” way the Scottish Parliament was set up left questions over who could authorise a vote.
Sturgeon attempts to stamp out speculation of legal action to force independence bid
It is absolutely essential that if the will of the Scottish Parliament is for a referendum then that should be respected
Scottish Lib Dem leader Willie Rennie had demanded answers, writing to the First Minister asking for “clarity on exactly what you are planning to do”.
But pressed on whether she would ask judges to making a ruling, the SNP leader said she would stick to “political” wrangling.
Ms Sturgeon told BBC Scotland: “It is absolutely essential that if the will of the Scottish Parliament is for a referendum then that should be respected.
Critics feared the First Minister was plotting a costly legal challenge
“I don’t think there is any need, nor is there any intention, to see a matter that should be settled politically end up in the courts.”
But Mr Rennie said the First Minister was “refusing to fully rule out court action”, accusing her of “tramping along a familiar nationalist path”.
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He added: “Keeping the option of court action means we are stuck with the SNP’s rat-a-tat-tat campaign for independence moving forward every day.
“The First Minister’s refusal to clearly rule out court action on an independence referendum shows she is increasingly desperate in her bid for independence.”
Opponents have branded her five-day visit a “global grievance tour” after she also used a speech in California to claim the Prime Minister’s decision to reject her demand for a vote was “not a sustainable position” and “a bit of a holding position”.
LIVE: Scotland reacts as Sturgeon gets her referendum Tue, March 28, 2017
A total of 69 MSPs voted to hold another referendum and 59 voted against
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Scotland's First Minister Nicola Sturgeon (R) reacts as she leaves the chamber following a vote on the second day of the 'Scotland's Choice' debate on a motion to seek the authority to hold an indpendence referendum at the Scottish Parliament in Edinburgh
Ms Sturgeon added: “There will be another referendum on Scottish independence, of that I am fairly certain.”
The First Minister was tonight due to take part in a question and answer session at the Women in the World summit in New York.
Hillary Clinton, Canada’s prime minister Justin Trudeau and actress Scarlett Johansson were also due to speak.
Earlier, Ms Sturgeon hailed an announcement that Marriott International plans to open seven new hotels in Scotland in the next four years.
The new hotels, which include the W Edinburgh at the St James scheme and three Moxy hotels, will boost the group’s room rate in the country by 75 per cent.