The team said it will review newly released documents in which Brown admitted to domestic abuse and "revisit" the issue when the team returns from London.
"The Giants do not condone or excuse any form of domestic violence. Josh has acknowledged that he has issues in his life and has been working on these issues through therapy and counseling for a long period of time," the team said. "We remain supportive of Josh and his efforts."
Earlier Thursday, the NFL announced that that it would review the documents as well.
Brown's admissions were revealed Wednesday by the King County (Washington) Sheriff's Office as part of his final case file, stemming from a May 2015 arrest following an incident with his wife, Molly Brown.
The sheriff's and prosecutor's offices initially decided to postpone the filing of charges, pending further investigation, with the sheriff's office recommending that the prosecutor's office file charges of two counts of fourth-degree domestic assault. Charges have not been filed.
In one of Brown's journal entries obtained as part of the investigation, he wrote, "I have abused my wife."
The league, which had already conducted its own investigation earlier this year and suspended Brown one game for violation of the league's conduct policy, said in a statement Thursday that it made repeated attempts to obtain any and all evidence and relevant information from the case.
The league's full statement reads:
"NFL investigators made repeated attempts — both orally and in writing — to obtain any and all evidence and relevant information in this case from the King County Sheriff's Office. Each of those requests was denied and the Sheriff's Office declined to provide any of the requested information, which ultimately limited our ability to fully investigate this matter. We concluded our own investigation, more than a year after the initial incident, based on the facts and evidence available to us at the time and after making exhaustive attempts to obtain information in a timely fashion. It is unfortunate that we did not have the benefit or knowledge of these materials at the time.
"In light of the release of these documents yesterday, we will thoroughly review the additional information and determine next steps in the context of the NFL Personal Conduct Policy. We will not be making any comments on potential discipline until that time."
An NFL Players Association source told ESPN's Jane McManus on Thursday that the union was not aware of Brown's journal entries that admitted abuse before they were revealed to the media.
Baltimore Ravens wide receiver Steve Smith Sr., who watched his mother suffer abuse when he was a child, took to Twitter to blast Brown and wrote, "what a shame NFL acts like it cares." Smith also has called out former Carolina Panthers teammate Greg Hardy in the past for his comments on domestic violence.
— Steve Smith Sr (@89SteveSmith) October 20, 2016
Former Giants quarterback Sage Rosenfels tweeted that the Giants should cut Brown.
I played for the New York Giants.
I respect so many people in that organization. But….
WHAT ARE YOU WAITING FOR???#cuthim
— Sage Rosenfels (@SageRosenfels18) October 20, 2016
Brown was on the practice field with teammates on Thursday afternoon. He has made 11 of his 12 field-goal attempts since returning from his suspension.
The Giants re-signed him to a two-year, $4 million deal this offseason. Co-owner John Mara said in August the Giants were comfortable re-signing Brown after reviewing all the information at their disposal.
Giants coach Ben McAdoo also said in August that he supported Brown "as a man, a father and a player."