Former First Minister Alex Salmond called on Ms Sturgeon seize on the turmoil at Westminster and push for a second vote - but other SNP luminaries such as Jim Sillars and Pete Wishart urged caution.
Ms Sturgeon has pledged to set out her plans for a second referendum in the coming weeks, insisting Scots must have an alternative to the Brexit turmoil a Westminster.
Mr Salmond today insisted it was time to seize on the weakness at Westminster.
“Nicola should be concentrating all her energies on the independence agenda where we will never have better circumstances,” he told the Sunday National.
“As far as I am concerned Westminster’s Brexit difficulty should be Scotland’s opportunity.”
Ms Sturgeon is to give an update to the Scottish Parliament on her plans in the coming weeks. A formal request for a Section 30 order which would give Holyrood the authority to stage a referendum was rejected by the UK Government last year, with Theresa may insisting “now is not the time” to revisit the Scottish constitutional issue amid the Brexit uncertainty.
And Mr Sillars, the former SNP deputy leader, warned there is “no appetite” for a second independence referendum.
“There is no national Yes organisation in place - a prerequisite to success as many Yes activists and voters are not SNP,” he told the Sunday Times.
“No policy work has been done on the psot-Brexit situation and thus we are not in a position to deploy then new polices in that post-Brexit new paradigm that will be needed to convince NO voters to vote Yes next time.”
Polls indicate there has been no rise in support for independence among Scots since the last vote in 2014 and Perth and North Perthshire MP Pete Wishart said a vote should be held when it can be won.
“We are already making progress towards that with Brexit as the catalyst,” he told the Sunday Times.
“But it will be difficult to secure the conditions to make a referendum happen before the next Holyrood election.”
Alex Bell, a former SNP Government adviser also called for a more considered approach.
“The SNP and Yes have to stop seeing independence as a sneaky prize to be won when everyone else is messing up and instead base their campaign on the reality of what Scotland can achieve through an honest understanding of the world.”
Ms Sturgeon had pledged to hold a second referendum in the immediate aftermath of Brexit but “reset” her plans after the SNP suffered heavy losses in the 2017 UK election when the constitution dominated the campaign.