The First Minister and SNP leader ruled out having a fresh ballot on the issue during the “acute phase of the pandemic”.
But having said already she would like to see a referendum take place in the first half of the next Holyrood term, Ms Sturgeon said that could happen “when we are clearly in the recovery phase”.
Her comments attracted criticism from the leaders of the pro-UK parties, with Scottish Conservative leader Douglas Ross saying: “This is the clearest sign yet that the SNP will put another referendum before Scotland’s recovery.”
He said: “Nicola Sturgeon talks of Alex Salmond being a betting man but she’s willing to gamble Scotland’s recovery on a reckless plan to break up the country.”
Mr Ross added: “The SNP’s obsession with independence is clouding her judgment.
“The last thing Scotland needs is more uncertainty and a new constitutional crisis on top of the health and economic crisis we’re facing.
“The Covid crisis will not end the day lockdown ends or when we finally defeat the virus.”
Scottish Labour leader Anas Sarwar argued that “holding a referendum during the recovery would be irresponsible”.
He stated: “Alongside the tragic death toll, we have taken an economic hit harder and deeper than the banking crisis.”
And he claimed that the SNP leader “has a blind spot when it comes to the constitution”.
Meanwhile Scottish Liberal Democrat campaign chairman Alistair Carmichael said that the SNP leader had “once again made it very clear that her only priority this election is another independence referendum”.
He added: “This is not what Scotland needs. Scotland needs a needle-sharp focus on green and secure jobs, a plan to help education bounce back and supporting the NHS and mental health.”
Ms Sturgeon, speaking on BBC Radio Scotland’s Good Morning Scotland programme, insisted that her “first priority” if she is re-elected first minister after May’s Holyrood election would be to “continue to lead the country through the Covid crisis”.
However she stated: “When we come out of that crisis yes I do think the country should have a choice of independence, so that decisions about our future lie here, not in the hands of Westminster governments led by politicians like Boris Johnson.”
Asked when a second independence referendum could be held, she said: “We have to come out of this crisis. I can’t, no more than anybody else across the globe can right now, give you a fixed date for when Covid will be over.
“Getting us though Covid has to be my priority.
“If we are out of the Covid crisis I would want to see an independence referendum be in the first half of this Parliament, because as we recover from Covid it’s really important we have the powers and the decision making here in Scotland to ensure we have the kind of recovery a majority want.
“That will be when we are not in the acute phase of the pandemic, when people like me are not having to stand up every day and report deaths and hospitalisations, when we are clearly in the recovery phase.”