WASHINGTON — Under fire from injured retirees who say they were denied sufficient benefits, the head of the National Football League Players Association asked Congress yesterday for greater authority to approve disability claims. The director of the players association, Gene Upshaw, said the union currently is limited in what it can do for the scores of former players who are battered and broken from years of playing the violent sport. At the same time, Upshaw and NFL Commissioner Roger Goodell said league pensions are improving.

“We have made great progress, and we are not finished,” Upshaw told a Senate committee. “Congress can help.”

It is the first time the union has asked Congress for help with the problem, which was the subject of a House hearing earlier this year.

Retired football players have been openly critical of the NFL and the players’ union over the amount of money that older retirees get from a $1.1 billion fund set aside for disability and pensions.

Goodell defended the system, saying the NFL is boosting benefits when many companies around the country are reducing them. But he acknowledged that there have to be ways to improve.

“We recognize this is not a short-term problem,” he said in his testimony.

Several former players testified — sometimes tearfully — about the injuries they now live with. Witnesses included Garrett Webster, son of the late Mike Webster, the Hall of Fame Pittsburgh Steelers’ center who suffered from mental illness that was widely attributed to head injuries.