In a message issued to staff yesterday he called on RBS workers not to be overwhelmed by speculation over the part-nationalised bank's future and to focus on improving customer service.
The New Zealander, who replaced Stephen Hester this month, is keen to draw a line under the bank's array of legacy problems.
He told the bank's 122,000 employees: "Most of you come to work every day to do your jobs for customers and are not consumed by the speculation that swirls around the bank."
RBS has been caught up in a range of scandals that has hit the sector including the fixing of key interest rates.
It is also understood to be one of the institutions being investigated over manipulation of foreign exchange markets. Newswire Bloomberg reported yesterday that an instant-message group involving senior traders at RBS, Barclays and Citigroup is being examined by regulators.
RBS has scaled back its investment bank in recent years and there are signs that Mr McEwan would like to trim it back further.
He told staff that issues that are now a small proportion of its activity had "taken up too much time of the management team".
He said: "Let's address the legitimate concerns shareholders and other stakeholders have. And then let's get on with building a great bank for customers."
The Edinburgh bank is awaiting the release of a report by investment bank Rothschild into the potential split of the lender into good and bad banks.
The report was requested by the Treasury in response to a recommendation by a parliamentary commission into the banking industry.
RBS previously signalled its opposition to such a split and under Mr Hester had a notoriously frosty relationship with the Treasury.
But Mr McEwan has adopted a more conciliatory stance and regards the review as a chance to put its problems behind it.
In his message to staff, the former RBS retail banking chief said: "The future of this company will not be about whether we operate in particular areas or where our problem assets sit. The future of this company is about how good a job we do for our customers."
An RBS source said: "The review has turned out to be a great opportunity. You have a brand new chief executive who has been handed a ready made mechanism for resetting our relationship with the Government and regulators."