Nicola Sturgeon has said a second independence referendum will become a “legitimate, almost necessary” step unless Scotland secures a special relationship with the European Union before article 50 is triggered.

The first minister used a speech in Edinburgh to accuse Theresa May’s government of putting the settlement that established the Scottish parliament under “grave threat” by rejecting Sturgeon’s calls for a special deal.

Sturgeon earlier wrote in an article for the Times that her moves towards a second referendum were prompted by the prime minister’s “sheer intransigence”, in a further effort to push May into fresh concessions.

May is under pressure from within her cabinet to counter Sturgeon’s agitation, increasing expectations the prime minister could set out what Scotland will gain from Brexit when she addresses the Scottish Conservative annual conference in Glasgow on Friday.

May has been publicly warned by two former prime ministers, Sir John Major and Tony Blair, that her quest for a hard Brexit threatens to trigger a second independence referendum.

Blair said earlier this month a hard Brexit would make Scottish independence “much more credible”.

In turn, there is growing speculation Sturgeon will use her conference speech in Aberdeen later in March to confirm she plans to table a new referendum bill at Holyrood, or demand the UK government gives Holyrood the powers to stage one.

Hinting again that she is on the brink of calling a new independence vote, Sturgeon told the David Hume Institute on Tuesday the prime minister had to prove that Scotland would have a bespoke deal before she triggered article 50 by the end of March.

Sturgeon said that if May failed to do so, then “proposing a further decision on independence wouldn’t simply be legitimate, it would almost be a necessary way of giving the people of Scotland a say in our own future direction”.

She added: “It would offer Scotland a proper choice on whether or not to be part of a post-Brexit UK.”

Ruth Davidson, the Scottish Tory leader, accused Sturgeon of deceiving voters since the UK government’s white paper on Brexit stated unambiguously that none of Holyrood’s existing powers would be removed. The document also suggested Holyrood would gain extra powers.

“This hyperbole from the first minister takes synthetic grievance to a whole new level. Frankly, she sounds shrill,” Davidson said.

“Nicola Sturgeon’s attempt to use Brexit to manufacture the case for a second referendum has quite simply failed.”