The Taoiseach has suggested that an all-party Oireachtas committee could examine ways of increasing the regulation of the gambling industry.
Micheal Martin also said the Government will consider a Labour Bill to ban gambling adverts.
Mr Martin said gambling addiction was a “terrible illness” that can destroy people and families.
Minister of State for Law Reform James Browne is to bring in comprehensive legislation this year to reform the gambling industry.
It will include the introduction of a gambling regulator.
Labour leader Alan Kelly said the volume of gambling ads shown during European Football Championship games were “frankly incredible”.
It comes days after Michael D Higgins said there are “serious questions” over the amount of sports gambling advertising in the media.
It was the second time in a number of weeks that the president has criticised advertising for betting.
On Tuesday, Mr Kelly called on the Taoiseach to implement Labour senator Mark Wall’s bill to ban gambling ads.
The Gambling (Prohibition of Advertising) Bill 2021 would ban all gambling ads across digital, print and broadcast media.
The impact that has on families are often hidden until it's too lateAlan Kelly
“The advertising that’s out there is incredible. It never stops,” Mr Kelly said.
“1.36 billion euro was lost to gamblers last year at 300 euro per person, but we all know that it’s really a large amount of money lost to a small amount of people.
“If we do not deal with this issue we’re going to continue to have the significant problems we have for so many people when it comes to an addiction to gambling, when it comes to mental health issues, and it comes to even suicide.
“The impact that has on families are often hidden until it’s too late.”
He said the plan to bring in a regulator is welcome, but was taking too long.
Mr Martin said the regulator will have the powers to regulate advertising, both online and through more traditional mediums.
“We will look at Deputy Wall’s bill and perhaps it would be important to have an Oireachtas all-party approach to this and engagement on it,” Mr Martin added.
“I think in the meantime, it’s important that we pursue the legislation in terms of the establishment of the regulator.”
He added: “He (Mr Browne) envisages the draft general scheme will go to the Government by the end of Q3 and intend to finalise the appointment of a CEO designate by the end of the year.
“The regulator will have the enforcement powers for licensing and powers to take action where individuals and operators are failing to follow rules and regulations, and it will have key objectives in terms of making sure to provide for responsible and safer gambling, combating problem gambling as well.
“I think addiction from gambling is a terrible illness, which can destroy families and destroy individuals.
“I am very conscious, particularly in terms of social media, the plethora and the proliferation of ads and its impact on young people, in particular, can be very damaging indeed.
“I think we need to wise up to that and to deal properly with it as a legislature.”
Mr Kelly said that gambling companies were “totally unscrupulous”.
“If people have a problem with gambling and they search gambling online, they’ll be flooded with ads for gambling,” he added.