The finance minister has described the behaviour of 16 Davy's employees as "outrageous" and has committed to strengthening the laws around the accountability of senior individuals.
Paschal Donohoe has also moved to ease concerns by stating that the decision to cut Davy as dealer in selling Irish Government bonds will have no impact on the State's ability to borrow.
It comes as calls grow to name the people involved in the Davy scandal after the Central Bank fined the stockbroking firm €4.1m for its failure to supervise a group of 16 employees as they profited in 2014 from personal dealings in the sale of Anglo Irish bank bonds.
Labour finance spokesperson Ged Nash said the Central Bank should investigate individuals involved and not just institutions.
Solidarity-PBP TD Paul Murphy said the scandal showed a "culture of greed and entitlement" in the financial sector.
The Government’s National Treasury Management Agency (NTMA), which organises sales of sovereign bonds for the State, has also struck off Davy from its roster of primary dealers just days before a €1.5bn auction in which the scandal-hit broker was due to play a key part.
However, Mr Murphy called on the State to end all other contracts it may have with Davy.
Social Democrats co-leader Catherine Murphy said she had tabled questions to the Taoiseach, Tánaiste and finance minister to find out if they have escalated the Davy issue to the gardaí.
"It's very clear that there's a lack of consequences. The fine to Davy is a consequence for the company, but it doesn't carry a consequence for the individuals.
"The 700 or so people who are employed by that company are badly let down by the fact that these 16 are not named because there's a question mark over every employee by virtue of there not being a naming of the individuals."
Ms Murphy also said that an anti-corruption agency is required to investigate white-collar crime.
Meanwhile, Mr Donohoe said the heads of bill to introduce senior level accountability will be brought to Cabinet before the summer.
"The behaviour that happened was outrageous. It is behaviour that fell so far yet again below the standards which we require of the financial sector. But there is a legal framework in place; I will strengthen that legal framework," Mr Donohoe said.
He added that the State's ability to issue debt and to continue with the borrowing needed to fund our response to Covid-19 will "not be in any way affected" by the decision that the NTMA took yesterday not to use Davy in those type of transactions in the future.
"We will be able to continue with the kind of activity that we need to support our country in dealing with the pandemic and supporting our public services," he said.