The first minister told BBC Scotland she would set out her next steps to the Scottish Parliament after Easter.
Ms Sturgeon has already said she does not intend to take the issue of a second vote on independence to court.
It follows the UK government's rejection of SNP plans to hold a referendum before Spring 2019.
Prime Minister Theresa May has argued that the focus of Brexit negotiations should be on getting the best deal for the whole of the UK.
Ms Sturgeon wants a referendum to take place between autumn 2018 and spring 2019.
She said: "I'm absolutely clear that the position of Theresa May, I just don't think is politically sustainable.
"If the Scottish Parliament is of the position, as it is because it has voted in this way, that Scotland should be given a choice - not now, but when the time is right, when there is clarity about Brexit and obviously when there is clarity also about independence - that we should have a choice about our future.
"I will set out, having written to Theresa May on the back of the Scottish Parliamentary vote, I've said sometime after the Easter recess, I've said I will set out what I consider the next steps to be, but I will set that out to parliament.
Responding to the possibility of court action or a snap election, Ms Sturgeon added: "These are not the kinds of things I am thinking of. I've got a responsibility to lead the country.
"I was elected as first minister less than a year ago. I've got a responsibility to lead this country.
"We are very focused on getting growth in our economy and transforming education. These are things that continue to be my priorities - these sort of scenarios that are put to me are not the ones I am thinking [of], but I do have an idea of how I progress the will of parliament."
The Scottish Conservatives said the first minister was "distracted" by the issue of a new referendum.
A party spokesman said: "Never mind a snap election, Nicola Sturgeon needs to go further and take the threat of an unwanted second referendum off the table.
"If the first minister's priority is really the economy and education, then we need to see some clear action on both fronts.
"While she has been distracted by constitutional wrangling, GDP figures have shown that Scotland is halfway to a recession while education reforms have been kicked into the long grass."
Scottish Labour also called for talk of another referendum to end.
The party's leader, Kezia Dugdale said: "Scotland is divided enough, we don't need, and don't want, another referendum on independence.
"Holding another referendum on leaving the UK is the wrong thing to do for Scotland's economy, especially when there is so much economic uncertainty from the Tories' reckless plans for a hard Brexit.
"The Labour Party I lead will never support independence and the unprecedented levels of austerity it would mean for our public services. We believe that together we're stronger."
Nicola Sturgeon has dismissed talk of a snap election at Holyrood to break the deadlock over a second independence referendum.