Sinn Féin's finance spokesperson Pearse Doherty has told the Dáil that there needs to be an immediate reduction in the cost of insurance policies.
Deputy Doherty was introducing the Judicial Council Amendment Bill to its second stage during Private Members Business.
The bill would force insurance companies to tell the Central Bank - each year, for the next four years - how the cost of claims has fallen as a result of the new Personal Injuries Guidelines, which came into effect on 24 April, this year.
Insurers would also have to outline how those savings are being passed onto customers.
The Personal Injuries Guidelines have reduced the cost of claims by an average of 50%, Mr Doherty said, and by up to 69%.
The same level of oversight included in the measures he is proposing is already in force in Britain, he added.
"We should not accept any less oversight for customers here in this State," he said.
"All we are trying to do here is to make the insurance companies live up to their promise," to pass on savings, he said, and he appealed for the Government to drop an amendment that it intends to table.
The Government's amendment will only delay the progress of the bill to its next stage by nine months, Mr Doherty said.
Minister of State at the Department of Finance Sean Fleming rejected that appeal, and moved the Government's amendment.
The Minister said the new Personal Injuries Guidelines were delivered, under the Action Plan for Insurance Reform, "seven months ahead of schedule".
He said that he and the Minister for Finance have been engaging with insurers to hold them to account, and to ensure that they pass savings on to policy holders.
This process will continue, he told the Dáil, and the Government will be introducing insurance legislation in the autumn.
The Government "will take on board in a positive manner the principles behind the bill" when they are drafting legislation, Minister Fleming added.
He said that the Sinn Féin bill "goes much further" than the measures in operation in the UK.
Ged Nash, Labour spokesperson on finance, told the Minister that "we cannot wait another nine months" to tackle the issue.
He also said that insurance companies' intent to deduct Covid-19 State subsidies from the cost of payments they make is a "travesty", and he urged the Government to address this.
"We have a fundamental market failure in insurance in this country," Mr Nash said.
Until the Government steps in to fix this, he said, Labour is happy to support the Sinn Féin motion.
Róisín Shortall, Social Democrats co-leader, welcomed the bill as "it aims to provide oversight", which is needed, she said.
She commended Mr Doherty's "tenaciousness" in tackling the insurance industry in a way the Government has failed to do.
Earlier, Deputy Doherty noted that the cost of motor insurance has risen 35% over the past decade while the cost of claims has fallen by 9%.
He added that Sinn Féin research shows that 58% of people who received a renewal quote since the guidelines came into effect have seen their premiums increase.
And yet they had made no claims over the previous year. Only 22% saw a reduction, he said. 1,300 people were involved in the research.
Under the Personal Injuries Guidelines, everyone who had not made a claim should have seen their premium fall, he said.
He believes that his proposals will ensure that this now happens.