RSA, best known in Britain for its More Than brand, also has major businesses in Canada, Ireland and Scandinavia.
Storm Emma, which hit Britain and Ireland in March, will cost RSA 40 million pounds ($54.23 million) on a pre-tax basis, Scott Egan told a media call.
"All regions were impacted...in Canada, poor weather has continued into April and early May," Egan said.
"Weather costs are likely to impact our H1 performance."
RSA did not give profit numbers in its first-quarter statement, but said that underlying profits were lower than a year earlier due to the higher bad weather costs.
Net written premiums rose to 1.52 billion pounds, however, helped by a move away from business where profitability was threatened, RSA said.
"We can't control the weather but most things we can control," Chief Executive Stephen Hester told the call.
Bad weather costs were 5.1 percent of net earned premiums, 3.1 points higher than a year earlier.
KBW analysts calculated the weather costs at 85 million pounds, below their 90 million estimate. They reiterated their outperform rating on the stock.
RSA's shares rose 2.55 percent to 652 pence at 0748 GMT, outperforming a steady FTSE 100 index <.FTSE>.
($1 = 0.7376 pounds)
(Reporting by Carolyn Cohn, Editing by Lawrence White and Adrian Croft)