Swiss group Zurich said it was determined not to overpay for RSA Insurance amid speculation it is working on a lower-than-expected offer for the 123.ie owner.
RSA saw shares come under pressure as figures revealing an 84% surge in half-year earnings were overshadowed by a report suggesting Zurich is considering an offer worth £5.4 billion, against hopes for at least £5.6 billion.
Zurich, which also posted its half-year results, said it saw "significant benefits" from a takeover of RSA, but added that "any capital deployment would need to meet the same hurdles that we apply to any other investment".
The European insurance giant said last week it was considering an offer for RSA, with reports suggesting a bid might be worth £5.6 billion, or 550p a share.
But it is thought Zurich is putting together a bid of around 527p, according to the Daily Telegraph.
RSA shares fell 2% at one stage, in spite of interim results showing group operating profits rose 84% to a better-than-expected £259 million compared to a year ago, driven by higher underwriting profits, fewer weather-related claims and stable investment income.
RSA has advised its shareholders to take no action as regards a potential bid from Zurich.
Shore Capital analyst Eamonn Flanagan said the release of RSA's robust half-year results meant the "gloves have come off and the bidding process can start in earnest".
He said RSA had "a superb number of assets around the globe", adding it may also be attractive to rivals such as Allianz and Generali.
RSA is run by chief executive Stephen Hester, the former boss at Royal Bank of Scotland, who was hired to revive the insurer's fortunes after it was hit by a series of profit warnings more than 18 months ago.
This came after an issue in the group’s Irish arm, where a £200 million black hole was discovered in the division's finances.
Since Mr Hester took over at RSA from his predecessor Simon Lee, he has sold a clutch of assets, overhauled the management and held a £775 million rights issue to rebuild the group's balance sheet.
RSA said today: "The intense pace of change over the last 18 months to make RSA better, stronger and more focused is now producing strong results."
The insurer said its underwriting profits in Britain were at their highest since 2006 due to a more disciplined approach and hit a 10-year record at its sizable Canadian business.
It added that over the last six months it has sold businesses in Hong Kong, Singapore, India and China. It also announced the disposal of its UK engineering inspection business, bringing its total agreed disposals to £835 million over the last 18 months.
The firm said it expected the insurance market to remain competitive, with the group having to make trade-offs between sales and strong pricing.
Mr Hester added: "Our goals for 2015 as a whole and beyond are unchanged - to make further strong and sustainable progress towards an RSA that is 'Focused, Stronger, Better'.
"We firmly intend to build a company that will thereby outperform for customers and for shareholders."
Half-year profits from suitor Zurich showed second quarter net profit falling 1% to $840m, impacted by losses within its general insurance division.