Chief executive Ross McEwan said there is "more to do" to turn around the 81% state-owned institution he has run since November and added that performance during the rest of the year will be affected by restructuring costs.
He said the bank will "make sure" it pays top staff enough to retain them despite the Government vetoing plans to offer bonuses above the level of the European Union pay cap.
RBS's income for the three months to the end of March was down 2% compared with the same period a year earlier at £5.1bn as it scaled back its investment bank.
Pre-tax profit of £1.6bn compared to £826 million the previous year, was well ahead of City forecasts in the absence of the sorts of mis-selling provisions and conduct costs that have marred previous financial results.
Mr McEwan said the figures "show the steady progress we are making" and illustrated the bank's potential when it is not dogged by one-off costs.
But he added: "We have more to do and plenty of issues from the past to reckon with".
RBS's expenses were 6% lower year-on-year at £3.2bn, due to what RBS described as "tactical initiatives". The bank has yet to reveal what impact Mr McEwan's strategic overhaul of the Edinburgh-based bank will have on job numbers.
Ulster Bank, which was badly affected by the Irish property crash, returned to profitability in the quarter for the first time in five years, Mr McEwan said.
After having had a torrid time in recent months, RBS's shares bounced back 25.1p or 8.2% on the day to close at 331.7p. This boosted RBS's market value from £34.7bn to £37.6bn
Mr McEwan cautioned that the bank had yet to start the major restructuring he has proposed to become a largely UK-focused retail and corporate banking institution. He said this would see costs rise in the coming quarters. He added a "small number" of employees in its investment bank and turnaround teams were affected by the decision of UK Financial Investments, which manages the government's stake in RBS, to oppose its attempt to get shareholder approval to pay bonuses above the European Union cap of 1005 of salary.
He said he understood pay is an "emotive issue".
"But it is a key time in our restructuring. It is important we stay in the pack rater and rather less stuck out on our own as we change this business," he added.
Mr McEwan gave a strong hint that RBS would instead seek to boost basic pay to retain staff.
He said: "We are not going to pretend this is ideal." He added: "My objective is to make sure we can pay these people so we can continue to perform and continue to have a very good business for out customers."
Mr McEwan played down fears of a housing market bubble as prices begin to rise across the UK.
"We do not think it is a bubble," he said. "What we are seeing is more people wanting to get in to the housing market. For five years they have stayed out of it."
He added: "It is up to banks as much as it is the regulator that we are controlling what is coming now to our books and we have customers who can repay."
Gary Greenwood, analyst at Shore Capital, said: "While 'one swallow doesn't make a summer', we believe that the Q1 2014 outcome represents an excellent start to the year for the group following recent disappointment."
Jasper Lawler, analyst at CMC Markets UK, said: "If the bank can continue to maintain steady profit growth while avoiding any large fines then the prospects could be good."