Scottish asbestos groups and trade unions are to demand that the Scottish Executive supports moves to ensure victims and families get compensation.
A total of 1,900 people die from asbestos-related diseases annually
They will meet Hugh Henry, deputy minister for justice, on Monday to ask him to back a bill which would help victims of asbestos-related disease.
It would make sure mesothelioma sufferers and their families are not denied their "rightful compensation".
A recent House of Lords ruling means that compensation may be cut.
More than 30 MSPs have already joined a campaign calling on the Scottish Executive to help protect victims.
A total of 1,900 people are said to die from asbestos-related diseases across the UK each year.
However, last week the Law Lords ruled that compensation to victims and their families should be reduced where responsibility could not be attached to a single employer.
A total of 32 MSPs, including Jim Wallace, former justice minister, have condemned the ruling.
They said it overturned the traditional Scots law approach to such cases and described it as a breach of natural justice.
Harry McCluskey, chairman of Clydeside Action on Asbestos, will meet Mr Henry on Monday to ask for his support.
He said: "Currently, many families of victims are being denied their compensation because the law states that if cases settle before the death of the victim, their families, who are also victims, are denied their individual compensation claims.
"This is absolutely abhorrent and we are demanding the executive support our proposals to amend the Damages (Scotland) Act 1976 to remedy this situation".
Frank Maguire, of Thompsons Solicitors, said: "We have provided the minister with a draft bill for him and the Scottish Executive to back.
"It is urgent because this unfairness is happening in cases of people dying even as we speak."
Ian Tasker, STUC assistant secretary, said the union fully supported asbestos groups on the issue.
An executive spokeswoman said ministers had been considering the "sensitive, difficult and complex matter".
She added: "Mr Henry has always made clear his profound sympathy for people suffering from asbestos-related illness and their families.
"In response to previous representations, new rules to speed up resolution of personal injury cases were introduced in the Court of Session in April 2003.
"Officials have recently met with solicitors representing asbestos groups to gain an understanding of both operational and wider implications of their proposals."