Brandon Wade, AP
FILE - In this Nov. 8, 2015, file photo, Dallas Cowboys' Sean Lee is assisted by team staff in the second half of an NFL football game against the Philadelphia Eagles, in Arlington, Texas.

PHILADELPHIA — Critics of the NFL's proposed $1 billion plan to settle concussion claims believe a league official's sudden acknowledgement of a link between football and the brain disease CTE is a game changer.

The settlement is being appealed by players concerned that it excludes future cases of chronic traumatic encephalopathy, or CTE — what they consider "the signature disease of football."

The deal announced by lead plaintiffs' lawyers and the NFL in August 2013 would instead pay up to $4 million for prior deaths involving CTE.

Jeff Miller, the NFL's senior vice president for health and safety, told a congressional panel Monday for the first time that brain research on former NFL players "certainly" shows a link between football and CTE. The league has long argued otherwise.

"Given that, the settlement's failure to compensate present and future CTE is inexcusable," lawyer Steven F. Molo wrote Tuesday in a letter to the federal appeals court in Philadelphia that is hearing his appeal.

The court heard arguments in November on the fairness of the settlement and was expected to issue an opinion in the high-stakes case soon. The NFL and lead plaintiffs' lawyers have said they do not want to incentivize suicide by offering future payments. CTE cannot yet be diagnosed in the living.

Miller, responding to questions Monday, referenced the work of Boston University neuropathologist Dr. Ann McKee, who has found CTE in the brains of 90 former pro football players.

"Well, certainly, Dr. McKee's research shows that a number of retired NFL players were diagnosed with CTE, so the answer to that question is certainly yes, but there are also a number of questions that come with that," Miller said.

The NFL had not previously linked playing football to CTE, a disease linked to repeated brain trauma and associated with symptoms such as memory loss, depression and progressive dementia. Players diagnosed after their deaths include Hall of Famers Junior Seau, Ken Stabler and Mike Webster.

The settlement would resolve thousands of lawsuits and cover more than 20,000 NFL retirees for the next 65 years. The league estimates that 6,000 former players — nearly three in 10 — could develop Alzheimer's disease or moderate dementia.

They would receive an average of $190,000, though the awards could reach several million dollars in the most serious cases, which include young men with Parkinson's disease or Lou Gehrig's disease.

Chris Nowinski, a former professional wrestler who runs the Concussion Legacy Foundation, noted that millions of children still play tackle football despite the suspected risks. The foundation seeks to study and prevent head trauma in athletes.

"If we actually believe that football is linked to CTE now, then how is the NFL underwriting (youth) tackle football when kids could just as easily play flag and not be exposed to the risk of CTE at such a young age?" he asked.

An NFL spokesman did not immediately return a message seeking expanded comment on Miller's remarks.