Police are considering launching a probe into the Royal Bank of Scotland's £12 billion rights issue, it was confirmed today.

Scottish National Party MSP Christine Grahame has written to Lothian and Borders Police, asking them to investigate whether shareholders were misled.

Her call comes days after the bank - which has its headquarters in Edinburgh - revealed it was on course for the biggest loss in UK corporate history as it expected to write down as much as £20 billion on the falling value of its assets.

Today Ms Grahame argued that the state of the bank's finances should have been known at the time of the rights issue last April.

She alleged: "If you are misleading people into thinking this is a stable investment, when at that stage it must be known the state of the bank's stock, if you are doing that, it's a criminal offence."

Ms Grahame has also written to Scotland's top law officer, Lord Advocate Elish Angiolini, with the allegation.

And the South of Scotland MSP said: "A member of the public is entitled to report something to the police if they think a crime has been committed.

"It's now up to the police to look at it with their particular remit and decide whether or not to bring their findings to the Lord Advocate."

A Lothian and Borders Police spokesman said: "We confirm receipt of a letter from Christine Grahame MSP and are considering the matter."

An RBS spokesman declined to comment.

Scotland's First Minister said he favoured an investigation by the Scottish Parliament into the wider issues.

"I'd rather favour a parliamentary investigation, not just into the Royal Bank of Scotland - that would be daft as the Royal Bank of Scotland is only one of hundreds or banks worldwide which has got into serious trouble - but into the financial sector," said Alex Salmond.

He told BBC TV's The Politics Show: "I think there should be an investigation.

"My only provision is that that investigation should include the regulators, should include the Financial Services Authority to ask them why they were asleep on the job, and also the politicians who were in charge of the regulation and the administration of the financial sector.

"So long as there is such an inquiry, in public, that looks not just at people in the financial sector who have some hard questions to answer, but looks at the regulators and the politicians as well, I would be thoroughly in favour of it."

Mr Salmond also said he did not believe the Royal Bank of Scotland needed to be fully nationalised.

The immediate priority was to do everything necessary to sustain the flow of credit at a reasonable price to industry and companies, said the First Minister.

"I don't think that anybody - not many people - would argue that long-term nationalisation would be a good option for the Royal Bank of Scotland or indeed many other commercial banks," he went on.

"Right now, whatever needs to be done to kick-start that flow of credit must be done."