Nicola Sturgeon has accused the UK Treasury of trying to "systematically reduce the Scottish budget" as talks over future funding arrangements appear deadlocked.

The Scottish First Minister has written to David Cameron to complain the UK and Scottish governments are not currently working on a "shared understanding" of one of the key principles behind proposals for further devolution.

The two administrations have been locked in protracted negotiations over the fiscal framework for the Scotland Bill, which sets out how the block grant will be altered when MSPs get new tax-raising powers.

The Scottish Government had been working to a deadline of February 12 for a deal to be agreed - although Ms Sturgeon said her deputy John Swinney is looking to see if there is any flexibility in this timetable.

The Scottish Government has already said it will submit a revised proposal "consistent with the principles of the Smith Commission" in the next few days.

Ms Sturgeon said: "Perhaps most importantly if a deal is to be reached, I am writing to the Prime Minister today, seeking to address what I consider to be the central issue of principle that is standing in the way of a deal - the fact that we are currently not working to a shared understanding of what no detriment means.

"It has become increasingly clear that what the Treasury seems to want to achieve is an outcome that would systematically reduce the Scottish budget as a result of our differential growth in population, even though the Scotland Bill gives us no additional powers to grow our population."

The First Minister said she had written to Mr Cameron "to ask him to confirm that he shares my understanding of no detriment".

She stated: "If he does, our negotiating teams can then get on with striking a deal which delivers no detriment, rather than doing what the Treasury seems to want to do, which is have a negotiation about how much detriment Scotland should agree to bear."

Both Ms Sturgeon and Mr Swinney have previously warned they will pull the plug on the Scotland Bill by recommending MSPs veto the legislation if the two governments cannot strike a deal on the fiscal framework.

They insist they are ''not bluffing'', with the SNP claiming a bad deal could cost Scotland billions of pounds in the long-term.

Ms Sturgeon said that in her view there was "no ambiguity" in what was meant by no detriment - that if Scotland's tax policy and economic performance matched the rest of the UK, the Scottish budget should be no better or worse off than without the new powers.

The Scottish Government believes a method known as per capita indexed deduction, which would take into account the fact that Scotland's population is growing more slowly than the rest of the UK, is the best way of meeting the no detriment principle.

The First Minister said that as the Barnett Formula is already adapted to take account of population, any additional risk on that front through the fiscal framework would act as a "double whammy".

She said: "The current proposal on the table from the Treasury, which has been described by them as a concession, would, by our estimation, and all else being equal, reduce the Scottish budget by almost £3 billion over the next ten years.

"That is simply not acceptable. It would mean Scotland having to grow receipts from income tax much faster than the rest of the UK just to stand still."

Ms Sturgeon said the Scottish Government supported the principle of taxpayer fairness, namely that changes to the tax burden on taxpayers in the rest of the UK in respect of devolved taxes should not affect Scotland's budget.

She sounded a warning to the UK Government over the promises of more powers made during Scotland's independence referendum, in light of the upcoming in/out referendum on EU membership.

"As we approach an EU referendum, people anywhere in the UK have a right to know that what the UK Government says in a referendum campaign can be trusted and will be delivered."

She added: "I hope that the Prime Minister and I can reach a shared understanding of no detriment that then clears the way for a discussion about how that can be delivered."

Mr Swinney has written to Bruce Crawford MSP, convener of Holyrood's Devolution (Further Powers) Committee, to see what flexibility there might be around the February 12 deadline, set to give MSPs enough time to scrutinise the deal.

Mr Crawford said: "Unfortunately, the committee's preferred date for an agreement of a fiscal framework by the end of this week has not been met.

"Although this is less than satisfactory, the committee will now need to address the reality that more time is needed to secure an agreement.

"This delay will potentially impact on the committee's ability to appropriately scrutinise any agreement.

"However, I know committee members will do everything they can to provide full scrutiny to the detail of any agreement that may emerge."

Downing Street confirmed they had received Ms Sturgeon's letter and said they would reply "in due course".

Asked if Mr Cameron was ready to meet the First Minister to seek a way of breaking the logjam, the PM's official spokeswoman said: "The Prime Minister has been fully behind the talks that are happening between the UK Government and the Scottish Government. He is engaging with it and he will keep doing that.

"But I think the focus will continue to be the talks between the Treasury and Ms Sturgeon and John Swinney."

The spokeswoman added: "We remain committed to implementing the Smith agreement in full.

"A deal has got to be fair to Scotland and it has got to be fair to taxpayers in the rest of the UK too.

"One of the issues the First Minister has highlighted is this definition of 'no detriment'. The point I would make is that 'no detriment' does not mean 'no risk'.

"I would note that John Swinney has himself accepted in the past that, around this issue of risk, it would be unfair for the rest of the UK to shoulder all the risk."

Labour's shadow Scottish secretary Ian Murray MP, said: "We welcome this move by the First Minister. At the weekend, we asked both parties to set out the principles they are following, and we are glad Nicola Sturgeon has done that today.

"We also welcome her shedding light on the areas where both parties continue to disagree. We have been calling for this kind of transparency since the negotiations began and we are also pleased that the Scottish Government is seeking more time to negotiate.

"We need a conclusion to this process that is fair to people in Scotland and that protects our public services now and into the future. We repeat our call today that Scottish and UK Ministers should not leave the negotiating table until a deal is done."

A UK Government spokesman said: "The UK Government is absolutely committed to implementing the Smith agreement in full and in line with the no detriment principle.

"The offer we have placed on the table would have delivered more funding for the Scottish Government than the existing Barnett formula since devolution in 1999.

"From the outset our position on the fiscal framework has been clear - we stand ready to do a deal that is fair for Scotland and fair for the rest of the UK."

A UK Government spokesman said: "The UK Government is absolutely committed to implementing the Smith agreement in full and in line with the no detriment principle. The offer we have placed on the table would have delivered more funding for the Scottish Government than the existing Barnett formula since devolution in 1999.

"From the outset our position on the fiscal framework has been clear - we stand ready to do a deal that is fair for Scotland and fair for the rest of the UK."