Following the meeting with the Prime Minister and other devolved leaders in Cardiff, Nicola Sturgeon said "the next few weeks are going to be really critical".
Her comments sparked speculation the SNP leader could issue a demand for a rerun of the 2014 ballot at her party's spring conference in March.
Ms Sturgeon insisted she needed to see "tangible evidence" that her plan for Scotland to stay in the single market while the rest of the UK leaves would be taken forward.
But Scottish Tory leader Ruth Davidson said it was more "sabre-rattling from an increasingly desperate First Minister".
She added: "It's clear she's running out of ideas on how to make Brexit about Scottish independence, and is now reduced to simply repeating the same hollow lines over and over again.
"Nicola Sturgeon should be using these talks to work with others from across the UK to get the best Brexit deal for all of us."
Nicola Sturgeon hinted a two-month deadline on a Brexit deal
The Scottish Government has also called for new powers over immigration to be devolved to Holyrood as part of its demands for a differentiated deal.
Once again Nicola Sturgeon has attended a meeting on Brexit and delivered nothing but threats about imposing another independence referendum
Kezia Dugdale, Scottish Labour
But UK ministers and experts have said the Norway-style package is unlikely due to the complexity of such a deal.
A communique issued following the two-hour meeting said consideration of the SNP's proposals, and those from Wales, would "intensify" between now and the triggering of Article 50 at the end of March.
But Ms Sturgeon said she "remained to be convinced" that what she called her "compromise" proposals were being taken seriously.
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The First Minister of Scotland held a meeting with Theresa May
The First Minister also claimed "there's no sign" of the UK Government meeting the "devolved administrations halfway".
She told the BBC: "The next few weeks are going to be really critical if we are to be convinced – and I'm far from convinced – that Scotland's voice is going to be heard or listened to at all."
Asked if this could see her announce another vote on independence by March, Ms Sturgeon said: "I'll do what needs to be done to protect Scotland's position.
"We are running out of time for this process. It can't go on indefinitely and it won't go on indefinitely.
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Nicola Sturgeon visits Glaxo Smith Kline.
"This is one of the last key opportunities for me to make clear to the Prime Minister that I have to see some movement on her part, and over the next few weeks she has got the opportunity to demonstrate whether that movement is going to be forthcoming."
Ms Sturgeon has previously vowed she will not hold a second independence referendum this year – but is pushing forward with a draft Bill that could pave the way for a poll.
This, however, is completely reliant on securing approval from the UK Government.
The Electoral Commission last year claimed that the SNP would have to wait at least nine months after passing the legislation.
Mrs Sturgeon is also pushing forward an independence referendum
Her predecessor, Alex Salmond, has predicted that a new referendum could be held in autumn 2018, before the UK leaves the EU, despite polls showing a majority of voters do not want another vote, and would not back separation.
The Joint Ministerial Committee (JMC) communique said the discussions were based on three main issues – exiting the EU, trade and investment opportunities and the "state of relations" between the devolved administrations.
It added that consideration of the Brexit plans put forward by Scotland, Wales and Northern Ireland was ongoing and would have to be "intensified"..
Scottish Secretary David Mundell confirmed "inter-governmental discussions" on devolved administration proposals would be intensified.
Nicola Sturgeon is hoping to get the best deals possible for Scotland
He said: "The question is not about can there be differentiation [for Scotland], the question is whether Scotland would benefit from differentiation, and that's what really has got to be at the heart of these intense discussions.
"Is it necessary to have a separate deal for Scotland, is the wish for a separate deal for Scotland driven by ideology or is it really based on economic fact and Scotland's future needs?
"That is what we need to have a full and frank discussion about in the weeks ahead."
Scottish Labour leader Kezia Dugdale said: "Once again Nicola Sturgeon has attended a meeting on Brexit and delivered nothing but threats about imposing another independence referendum on the people of Scotland.
"Nicola Sturgeon previously claimed that she would study the opinion polls to determine when she would hold another referendum, but public opinion couldn't be clearer. People in Scotland don't want another independence referendum."