The New York Giants released Josh Brown on Tuesday, admitting fault in their own response to the domestic violence allegations that have jeopardised the veteran kicker's NFL future.

Brown, 37, was suspended for the first game of the 2016 season after a May 2015 domestic violence arrest came to light.

But new information obtained from police by NJ.com last week claims that Brown had admitted abusing his wife, Molly, on multiple occasions.

That news prompted the NFL to put Brown on the commissioner's exempt list and the Giants to remove him from their travel roster for Sunday's game against the Los Angeles Rams in London.

"We believed we did the right thing at every juncture in our relationship with Josh," team president John Mara said in a release. "Our beliefs, our judgments and our decisions were misguided. We accept that responsibility."

Earlier on Tuesday, Brown released a statement via ESPN denying that he hit his wife but apologising for his behaviour.

"I have taken measures to get help so that I may be the voice of change, not a statistic. It is important to share that I never struck my wife, and never would," he said. 

"Abuse takes many forms, and is not a grey area. Through the past several years I have worked to identify and rectify my own behaviours. The road to rehabilitation is a journey and a constant modification of a way of life.

"My journey will continue forever as a person determined to leave a positive legacy and I embrace the opportunities to show and speak about what has helped me to be that man."

Brown also apologised to the Giants and Mara in particular. The team and its president had drawn criticism for backing their kicker publicly after allegations against Brown surfaced.

"We hope that Josh will continue to dedicate himself to rehabilitation, and to becoming a better person and father," the Giants' statement read. "We will continue to support him in his efforts to continue counselling, and we hope that Josh and his family can find peace and a positive resolution."