Zurich Insurance has announced that it has finished its discussions with RSA and does not plan to make a bid.
The Swiss insurer announced in July that it was considering buying its British counterpart for £5.6bn.
RSA said that the approach had been unsolicited but that Zurich`s decision not to proceed had not been a result of anything unexpected in the due diligence process.
Zurich warned profits in its general insurance arm would miss forecasts.
"Given the deterioration in profitability in certain parts of the General Insurance business, and following his appointment as General Insurance CEO, Kristof Terryn is conducting an in-depth review of the business," Zurich said in an update on third quarter trading.
It estimated that it would lose about $275m (£177m) as a result of the explosions at a container storage station in the Port of Tianjin in China in mid-August.
Overall, it expects an operating loss of about $200m from the general insurance business.
RSA shares fell 22% in early trading as some banks and investment houses advised clients to be less enthusiastic about the stock.
The falls came despite the company announcing that its trading results for July and August had been "positive and ahead of our expectations".
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