National said the decision to send the agreements out for more consultation showed FPAs had been "kicked for touch".
A working group, headed by former National Party leader and prime minister Jim Bolger, delivered its report in December 2018.
The union movement sees the agreements as a core promise to address what they claim is a "race to the bottom" in certain industries, where employers compete for business by driving wages down.
"We will find it most unsatisfactory if they don't deliver on what was quite an important promise and commitment," Council of Trade Unions president Richard Wagstaff said earlier this week as he urged the Government to "get on with it" and introduce legislation to enable the agreements.
Thursday's release does not lay out a timetable for legislation. Lees-Galloway's statement said the consultation was seeking feedback "on policy design features" of the agreements.
"Fair Pay Agreements would be an important addition to our employment law, and the Fair Pay Agreement Working Group gave us a solid foundation to work from. The Government wants to explore their recommendations and wider options to ensure we develop an accessible and workable system that offers benefits for all parties involved.
"Many working New Zealanders are not receiving their fair share. For a number of decades we have experienced increasing levels of inequality and poverty. Over that time, vulnerable workers have had less access to collective bargaining, and wages haven't kept up with productivity increases."
National's workplace relations spokesman Todd McClay said Labour appeared to have decided not to pursue a law change.
"The Government's clearly quite rattled by the concerns of the business community. It's really winding the unions up and putting it out to consultation after a very, very expensive and extensive working group is just them kicking it for touch if you ask me.
"Actually, we're not going to see any legislation before next year. I think they have given up because there won't be time to get this through Parliament before the next election."
While NZ First has successfully lobbied for earlier labour law changes to be watered down, McClay said he believed in this case the Prime Minister's office was deliberately slowing down the development of FPAs.
"I think in the end Labour's gone cold. I understand that the ninth floor [of the Beehive] has sent directions to the minister [Lees-Galloway] to slow-play this because they know it's harmful to their re-election chances."
Employer groups have also lobbied against the agreements. In the working group, members who represented employers refused to back the recommendations, in particular that once an agreement was reached it would be compulsory.
The consultation runs until the end of November.