David Cameron announced the change along with several other measures aimed at tackling the UK's 'compensation culture' in a speech to small business owners in Maidenhead.
A Downing Street spokesman told Out-Law.com that although there was no immediate timeframe for the change, an announcement would be made "in the near future".
Removing strict liability for civil damages under some existing health and safety regulations was one of a number of recommendations made by Professor Ragnar Löfstedt of King's College London in an independent report on health and safety laws last year. As a result of the report the Government announced in November that it would be consulting on abolishing "large numbers" of existing health and safety rules.
Cameron also suggested that the demands made by insurance companies on businesses could be forcing them to take steps far beyond what is actually required by the law to secure insurance cover.
He said that the Government would ask the major insurance companies to set out how they intended to deal with the problem, and would invite them to a meeting at Downing Street next month for further discussions.
Other changes announced included extending the scheme that caps the amount that lawyers can earn from small value personal injury claims to public and employers' liability claims. Capping lawyers' fees at £25,000 would, Cameron said, help deter "speculative" claims against businesses that would appear not to have done anything wrong.
The current fee cap is £10,000, but it only applies in road traffic cases.
Cameron spoke of an "excessive" health and safety culture that had become an "albatross around the neck of British businesses".
"Talk of 'health and safety' can too often sound farcical or marginal. But for British businesses – especially the smaller ones that are so vital to the future of our economy – this is a massively important issue. Every day they battle against a tide of risk assessment forms and face the fear of being sued for massive sums," he said.
Health and safety law expert Kevin Bridges of Pinsent Masons, the law firm behind Out-Law.com, said that while Cameron's proposals made good business sense some of his comments were "unhelpful".
"The Prime Minister said that health and safety is a monster. I disagree. The existing framework, whilst in need of some tweaking here and there, is fit for purpose in helping to prevent death, injury and illness at work. Ensuring a safe and healthy workforce is positively good for business," he said.
"The Government should indeed be focusing its efforts not on the number of health and safety regulations there are but on tackling the perceived compensation culture in this country that makes local authorities and employers generally risk averse," he said. "Capping fees in personal injury cases, removing strict liability for civil claims and encouraging insurance companies to take a pragmatic approach in their demands when it comes to providing insurance cover, will have a far greater impact on business in terms of what it needs to do to comply with the law and improve safety than reducing the number of laws there are."
Legal costs expert Keith Levene, also of Pinsent Masons, said that the move was part of an ongoing Government trend to tackle the spiralling costs of relatively low value personal injury and clinical negligence cases, particularly in the public sector and NHS.
A report by Lord Young into the 'compensation culture' last year recommended introducing a simplified personal injury claim procedure similar to that currently available in road traffic cases, he said.
"What David Cameron is saying here is that the Government are now going to look more closely at claims being made against the public sector, to ensure the costs being awarded are proportionate to the relative value of the claims themselves," Levene said.