Shares in the home and motor insurer, best known in Britain for its More Than brand, rose more than 5 percent after it reported a strong performance last year across most of its main businesses in Britain, Ireland, Canada and Scandinavia.
Chief Executive Stephen Hester, the former boss of British bank RBS (RBS.L), has cut costs and sold assets since joining RSA in 2014 with a brief to turn it around following an accounting scandal at its Irish division.
Zurich pulled out of a 5.6 billion pound ($7 billion) bid for the company in September 2015, due to problems in its own business, and Hester said RSA was doing fine alone.
"Our shareholders are benefiting significantly from not having sold to Zurich," he told a media call.
He added there were no bids on the table for RSA, and the firm "does not need a deal".
"If something came along, it would need to be additive to be of interest, rather than a substitute for what we are doing," he said.
Merger and acquisition talk has been swirling around European insurance markets due to strong competition in the sector and low interest rates, which have hit investment income.
Italian bank Intesa Sanpaolo has said it is studying a possible combination with Assicurazioni Generali (GASI.MI), Italy's biggest insurer.
RSA has no plans to sell more of its businesses, Hester told Reuters by phone, after a recent deal to offload legacy business - closed to new policyholders - to Enstar (ESGR.O).
"There's nothing meaty on the stocks," Hester said.
RSA posted a 25 percent rise in 2016 operating profit to 655 million pounds and raised its target for return on tangible equity to 13-17 percent from a previous range of 12-15 percent.
Its shares were the second best performer in the FTSE 100 index .FTSE at 1320 GMT, up 5.5 percent at 609 pence, after earlier hitting 617.5 pence, their highest since July 2011.
RSA "has again shown real progress", RBC analysts said in a note, reiterating their "perform" recommendation on the stock.
The insurer said it would pay a final dividend of 11 pence per share and total dividend of 16 pence, up 52 percent from a year earlier and above a forecast 15.1 pence.
($1 = 0.8042 pounds)
Reporting by Carolyn Cohn; Editing by Keith Weir and Mark Potter