Minister for Transport, Tourism and Sport Shane Ross has said he is "very optimistic" that the Judicial Appointments Commission Bill will be through by the summer.
He described it as a very serious requirement of the Independent Alliance in the Programme for Government.
On Friday, the bill was criticised by Attorney General Seamus Woulfe as a "dog's dinner" and who said some amendments to the bill were "contradictory", and "unconstitutional".
Speaking on RTÉ's This Week, Minister Ross said what the Attorney General is saying is very important and has probably been misunderstood, adding that "he (Mr Woulfe) said that some of the amendments give him constitutional concerns and he is saying that some of them are contradictory."
Minister Ross said he spent this morning with the AG, who is working on these particular amendments now and that they are going to be addressed tomorrow morning.
Minister for Finance Paschal Donohoe said he believes there are "considerable difficulties" with the bill, as it is currently drafted.
When asked on the same programme, if he would agree that the current system is "rotten" as suggested by Minister Ross, he said: "I believe it is a system that needs to change.
"This is a Programme for Government commitment, and I as much as any other government colleague, including Minister Ross want to see this change and we will change it."
There are "core features" of how he wants to change this, including setting up a commission that has a role for lay expertise, Minister Donohoe added.
Separately, Opposition parties (Fianna Fáil and Social Democrats) have called on the Government to urgently clarify reported remarks made by the Attorney General in relation to an ongoing court case.
The remarks were made during an "off the record" questions and answers session.