Tony Blair says he is hoping to change a ruling that will stop widows receiving full compensation for their husband's deaths from asbestos.
Mesothelioma causes damage to the lungs
Last month's Law Lords ruling will affect thousands of widows, whose husbands died from mesothelioma.
Firms had challenged a judgement favouring bereaved families and workers who contracted mesothelioma at work.
But Mr Blair said he hoped to make an announcement on his plans to change the House of Lords ruling in a fortnight.
"I regret that judgement. I'm looking at the moment to see the best opportunity for us to change it," he told a GMB conference in Blackpool.
"If we can change it, we will. I hope to announce something on this in a couple of weeks."
Mr Blair made the comments after he was pressed about the issue during a question and answer question at the conference.
Mesothelioma is a form of cancer that attacks the lining of the lungs - and the only known cause in the UK is exposure to asbestos.
In the appeal, insurers sought to limit an employer's liability to pay damages in cases where a worker may have been employed by several firms, none of whom can be specifically blamed for the onset of the fatal illness.
They argued that an employer's liability should be a proportion of the total compensation, to reflect the extent to which it contributed to an employee's exposure to asbestos.
In 2002 Law Lords ruled that an employer who negligently exposed a worker to asbestos could be held 100% liable - even if the employee had worked for several companies and it could not be proved which of them had caused the illness.
About 1,900 people die in the UK each year from mesothelioma.
The appeal raised the question of whether compensation should be denied altogether when a mesothelioma sufferer was in contact with asbestos during a period of self-employment, even if they were also exposed to asbestos in a different period as an employee.
The test case of Sylvia Barker, 58, of Holywell, Flintshire, was at the centre of the dispute.
The widow was awarded £152,000 in the High Court three years ago for the death of her husband, Vernon, who died aged 57, in 1996.
Mr Barker had worked for John Summers and Sons at the Shotton steelworks on Deeside.
He had been exposed to asbestos while he was employed there as well as for another company and for short periods during 20 years of self-employment.
Her damages will now be reassessed by the High Court to reflect the proportion of blame attributable to his time with Summers rather than 100% liability for his illness and death.
The Lords' 4-1 majority judgement also covered two other appeals.
The case of John Murray, who was employed by British Shipbuilders (Hydrodynamics) for 52 years, was considered, as was that of John Patterson, who died in May 2002 having worked with asbestos for much of his working life until his retirement in 1974.
In both cases insurers argued that, on a "time exposed" basis, they should pay only a proportion of the damages.
The awards in both cases will now go back to county courts for reassessment.