The reigning AFL premiers are facing damning claims, most notably against Kelly, that have been lodged in the Federal Circuit and Family Court of Australia.
Mark Cleaver, Collingwood's former head of First Nations strategy, is the sole applicant in the documents, while the Magpies are the only respondent.
Browne on Wednesday addressed the allegations, saying Collingwood would "fight these proceedings" and denied the club had a racism problem.
"We implemented all 18 recommendations from the Do Better report," he said.
"We are the only club that opened ourselves up for external investigation.
"When I came in as president I committed to prosecuting and implementing all of those 18 recommendations.
"Racism and discrimination is a fight that goes on day by day. It never ends. It's something we're very conscious of here.
"But the culture in this place as a result of adopting the recommendations from the Do Better report is vastly improved.
"It's a culture where people feel safe, people of diverse backgrounds feel safe and they feel safe to make complaints if they choose."
Browne could not have been any stronger in backing Kelly, who took over as Collingwood chief executive in January 2023, to continue in his job.
"From my experience, he's doing an outstanding job as a CEO of this football club," Browne said.
"He has the full support of the board and my full support."
Craig Kelly took over as Collingwood CEO in 2023. (Diego Fedele/AAP PHOTOS)
Cleaver worked at Collingwood for six months and Browne said his employment was terminated for reasons unrelated to the complaint lodged in court.
The Magpies say Cleaver first raised the matter in March, with the club then looking into the concerns."In addition to the internal process which took place, an external expert was engaged to review the findings. Both processes found no breach of workplace law," Collingwood's statement read."Following the conclusion of both processes, the former staff member made further allegations to Victoria Police, which examined them and determined not to take any further action."
Cleaver's legal representative said the allegations called into question whether Collingwood had "learned anything from its multiple self-inflicted racism scandals.
"We are entitled to expect more from a club that has promised to do better," Daniel Victory, principal with Maurice Blackburn Lawyers, said in a statement to AAP.
"The conduct alleged in this case has no place in society or any sporting club and especially not in a league that holds itself out as an agent for social change.
"Football fans have a right to feel let down once again by the Collingwood Football Club.
"The AFL should consider penalising premiership points from clubs if allegations like this are proven."
Speaking on Wednesday, Victory alleged Cleaver was subject to "racist and ableist incidents" during his six-month tenure working at Collingwood.
"My client's seeking compensation for economic loss and hurt, humiliation and distress," he told ABC Radio.
In 2021, the Magpies released an independent review to deal with racism.
Former president Eddie McGuire labelled the release of the Do Better report "a historic and proud day".
A week after his highly criticised comments, McGuire stood down following more than 20 years in charge.
AFL spokesperson Jay Allen said the league's integrity unit was aware of a human resources workplace complaint by a Collingwood employee.
