RBS could "adapt" its business in the event of Scotland's independence, bank chief executive Ross McEwan has said.
His comments came after UK Business Secretary Vince Cable said RBS would "inevitably" move its headquarters to London if Scotland became independent.
Mr McEwan said he had not discussed that possibility with Mr Cable, in the event of a "Yes" vote in the 18 September referendum.
The bank boss made his remarks in an online Q&A for the Guardian.
Mr Cable previously told a committee of MPs that, under independence RBS - bailed out by UK taxpayers to the tune of £46bn in 2008 - would want to be based where it was "protected against the risk of collapse".
The Scottish government described the comments about the bank, founded in Edinburgh in 1727, as "ridiculous".
Mr McEwan said: "We've been in Scotland for nearly 300 years. So I need to take this independence issue very seriously.
"It's really important that the Scottish people get the opportunity to vote, and then if I need to adapt my business to serve England, Scotland, Wales and both the Republic of Ireland and Northern Ireland, then I will."
He added: "Mr Cable and I have not talked about moving our head office."
Mr McEwan's comments came after Barclays chief executive Antony Jenkins told the BBC his bank "can make it work" if Scotland became independent.
A spokeswoman for the UK government's Department of Business, Innovation and Skills said that Mr Cable had been discussing a hypothetical post-independence scenario with MPs, "where there was no monetary, fiscal or banking union" between Scotland and the rest of the UK.
The spokeswoman added: "The Scottish financial services industry has developed in the context of a single fiscal union across the UK.
"As the UK government and independent commentators have stated, one possible outcome of independence is that the Scottish financial sector would reduce in size and status.
"This would happen if firms themselves react to heightened risk by structuring themselves such that they were no longer headquartered in Scotland."
In September's referendum, voters in Scotland will be asked the Yes/No question: "Should Scotland be an independent country?"