When the N.F.L. Players Association agreed in March to cut payments to some of the league’s most vulnerable former players by reducing their disability benefits starting Jan. 1, 2021, the decision was met with outrage and legal challenges from retired players and their families.

On Tuesday, the union said that deadline to reduce those payments had been extended by three years.

In a statement, the union said its executive committee and board of player representatives had voted unanimously to amend the current collective bargaining agreement so that the 400 or so players who now receive benefits for being totally and permanently disabled will not have their benefits reduced by roughly $2,000 a month until the start of 2024.

Those players, who have been deemed unable to work because of injuries they sustained in the N.F.L., receive up to $138,000 a year. That amount was to have been reduced by the value of their Social Security disability benefits, which amount to $2,000 or more per month.

The union’s willingness to agree to team owners’ demand for a reduction in benefits was heavily criticized on social media by the wives of former players on disability. Eric Reid, a free agent safety who last played with the Carolina Panthers, also criticized the union, and his lawyers wrote to the Players Association demanding an explanation.

In May, the union president, J.C. Tretter of the Cleveland Browns, said the N.F.L.P.A.’s 11-member executive committee and leaders from among retired players would re-examine changes to the Total and Permanent Disability benefit “to fulfill our obligation to all of our members.” He said the group had “a responsibility to review issues where we have fallen short.”

In July, two former players who receive these benefits, Aveion Cason, a running back who played for eight seasons, and Don Majkowski, a quarterback for 10 years, sued the league and the players’ union, as well as the medical board those institutions jointly control, for agreeing to reduce the disability payments they were granted for life.

Paul M. Secunda, a lawyer representing Cason and Majkowski, said they were “still considering what impact this development has for our litigation” and that they are “dismayed” that the union and league “did not reach out to us to let us know this was in the works, as it directly impacts the Class we seek to represent.”

It is unclear which entity will cover the continued benefits for three more years. But lawyers who represent former players and have been critical of the union for its willingness to cut the benefits of former players said the union leadership should be complimented for working out an extension.

“They deserve credit because it’s not easy, after an extraordinarily hard-fought negotiation where concessions had to be made, to delay this long enough to straighten it out,” said Brad Sohn, who represents numerous former players. “I’ve spoken to families who were really stressed out about this, and now they can breathe easier.”