At an emergency British Irish Council summit, Ms Sturgeon welcomed a suggestion by Welsh First Minister Carwyn Jones that the deal should be supported by Holyrood, the Welsh Assembly, Stormont and Westminster.
Her insistence that the process of Leaving should be given Scottish Parliamentary approval will fuel fears that Ms Sturgeon could hold the rest of the UK to ransom when it comes to triggering Brexit.
But Ms Sturgeon also found herself at loggerheads with the Northern Ireland First Minister Arlene Foster who said the UK-wide vote to Leave the EU had to be respected.
Both Scotland and Northern Ireland returned majorities for Remain, a position which led to Ms Sturgeon saying Scotland’s relationship with the EU should be protected and renewing her calls for a second independence referendum.
But Ms Foster, whose Democratic Unionist Party supported Brexit, was adamant that “the decision to leave was a UK wide one and we have to respect it.”
The summit in Cardiff was called by Mr Jones in response to the Brexit vote. Like England, Wales recorded a Leave vote. Mr Jones said Article 50 – the legal process by which member states quit the EU – had to be triggered before next summer.
Otherwise, Mr Jones said, there was a risk Leave voters would think the referendum result was being ignored.
Mr Jones added, however, that any deal should be approved by all three devolved administrations as well as Westminster.
“My view is that any future deal the UK agrees should be ratified by all four parliaments within the UK in order to get the greatest buy-in,” Mr Jones said.
The Welsh First Minister said they could not be “mere consultees” and had to be “very much part of that negotiation”.
Ms Sturgeon said Mr Jones had made a “very legitimate suggestion” that the decision to invoke Article 50 “should require approval in all parliaments in all devolved administrations”.