The bank made the remarks as it posted an attributable profit of £707mln for the first quarter, down from £808mln a year ago.
Total income dropped to £3.04bn from £3.30bn last year, reflecting declines in personal and commercial banking.
The net interest margin – the difference between interest earned on loans and money paid on deposits – fell to 1.89% from 2.04%, squeezed by a competitive mortgage lending market.
Net loans to customers increased to £306.4bn from £303.8bn while customer deposits rose to £355.2bn from £354.5bn.
Operating expenses dropped to £1.94bn from £2.01bn last year as litigation and conduct costs declined. Impairment provisions fell to £3.1bn from £4.2bn.
RBS said it remains on track to meet its £300mln cost reduction target this year, having saved £45mln in the quarter.
However, the cost to income ratio rose to 63.4% in the quarter from 60.5% last year.
Risk weighted assets edged down to £190.8bn from £202.7bn.
The common equity tier-1 capital ratio was stable at 16.2%.
In morning trading, shares dropped 5% to 237.2p.
"In summary, this statement could be seen as softening the market up for a profit warning later in the year," said AJ Bell investment director Russ Mould.
Ross McEwan's departure
The results come a day after RBS announced that chief executive Ross McEwan will step down after five-and-a-half years in charge of the taxpayer-owned lender.
McEwan, who will stay in the role until a successor is found and gets their feet under the desk, said it was time to leave as he felt he had completed the turnaround for which he was hired.
RBS, which received a £45.5bn bailout from the government during the financial crisis in 2008 and is still 62%-owned by the state, returned to the dividend list in February after last year saw it make a first profit for nine years.
Graham Spooner, investment research analyst at The Share Centre, said the bank's outlook should not come as a major surprise but it does "once again focus minds of investors who have become fatigued with Brexit on the possible consequences".
"We continue to recommend the shares as a ‘hold’ for investors seeking growth, willing to accept a medium level of risk but emphasise the need for patience," he said.