The bank, still 62.4% owned by the taxpayer, saw bottom line profit fall 12.5% to £707 million in the three months to March 31.
Pre-tax operating profit also came in lower at £1 billion versus £1.2 billion as RBS was hit by stiffer competition in the mortgage market and continuing uncertainty among businesses, with many reining in spending as Brexit fears linger.
The results come a day after RBS bosses warned at the bank’s AGM over a Brexit hit as uncertainty weighs on the economy.
Chairman Sir Howard Davies told shareholders that worries over the EU departure were hampering economic growth, which will take its toll on the bank’s performance.
Outgoing chief executive Ross McEwan said: “This is a solid set of results set against a highly uncertain and competitive backdrop.
“We continue to support our customers through this Brexit uncertainty while investing and innovating in digital services to meet rapidly changing customer needs.”
In October, RBS set aside £100 million to reflect the “more uncertain economic outlook” in Britain ahead of Brexit.
On Friday, the group said that while it is retaining its full year guidance, the “ongoing impact of Brexit uncertainty on the economy, and associated delay in business borrowing decisions, is likely to make income growth more challenging in the near term”.
Nevertheless, profits came in ahead of consensus estimates.
The figures also show that RBS shed £45 million in costs over the quarter and is on track to take £300 million out of the group by the end of the financial year.
RBS is having to come to terms with the departure of Mr McEwan, who announced his departure on Thursday - his resignation coming after more than five-and-a-half years at the helm.
He has a year’s notice period and will stay in the post until a successor has been appointed, and to ensure an “orderly handover”.
The New Zealander said he had achieved his strategy set out when he joined the bank, having returned the bank to profitability and put it on a firmer financial footing.
Sir Howard said the search for Mr McEwan’s successor will start immediately, with the bank casting the net internally and externally.
Alison Rose, who was recently promoted to deputy chief executive of NatWest Holdings, is seen as the leading internal candidate to take over from Mr McEwan.