(CNN) -- Former Minnesota Viking and outspoken same-sex marriage supporter Chris Kluwe said Monday he is encouraged the NFL team is looking into his claims that he was released in May because he is an LGBT activist.

Kluwe told CNN's Anderson Cooper 360 in his first television interview since being kicked off the team that he is confident an investigation will uncover the truth.

Over the past couple of years, the former punter has become known for his gay-rights activism, and in an article published Thursday on the website Deadspin he claimed he was fired by "Two Cowards And a Bigot" for his stance and not entirely for his performance on the field.

"I don't have anything against the Vikings organization itself. I had eight wonderful years with the Minnesota Vikings," Kluwe told CNN. "I had a problem with three individual people within the Vikings, and the fact remains is that I did everything my coaches wanted me to do (on the field). ... No one ever told me that I wasn't doing what I was supposed to do.

"The only thing that changed from Year 8 to when I got cut is that I started speaking out on same-sex rights."

The three individuals Kluwe referred to are Mike Priefer, the Vikings special teams coach; former head coach Leslie Frazier and Vikings General Manager Rick Spielman.

Priefer, the man Kluwe labeled a "bigot," denied the former player's claim in a statement to the StarTribune of Minneapolis.

"I want to be clear that I do not tolerate discrimination of any type and am respectful of all individuals ... The comments today have not only attacked my character and insulted my professionalism, but they have also impacted my family," said the coach, who has been with the team for two of his 11 years in the NFL.

Kluwe said that he decided when he began to work with Minnesotans For Marriage Equality was that he wasn't going to back down from people who told him to keep his views to himself. He never thought about stopping even after Frazier requested he stop speaking out.

"I said, 'Well, no. That's not the right thing to do. We are all American citizens. We all deserve to live our lives free of oppression,'" Kluwe told CNN.

The Vikings said in a statement Thursday: "Any notion that Chris was released from our football team due to his stance on marriage equality is entirely inaccurate and inconsistent with team policy. Chris was released strictly based on his football performance."

In his final season, Kluwe, 31, ranked 17th among punters in the 32-team league, averaging 39.7 net yards per punt. This season, the Vikings' Jeff Locke, a fifth-round draft pick, was 18th with a 39.2 yard average.

Kluwe said that after the Vikings drafted Locke in April he knew he was done with the team so he kept notes of his interactions with team officials.

"I realized I need to get all this stuff down now while it's fresh and make sure I have it because this is a story I would like to tell later," he said.

As a result of telling his story in the Deadspin article, Kluwe believes his time in the NFL is over. After he was cut, he had a tryout with the Oakland Raiders but didn't get the job.

He said speaking publicly about team matters was, in this case, like throwing a stick of dynamite on a bridge -- one that can never be crossed again.

But he thinks the Vikings investigation will reveal the truth, if his former teammates are given the opportunity to maintain anonymity when they are interviewed about what they witnessed.

He likely won't sue the team, he said, reiterating that he believes it was Priefer, Frazier and Spielman that moved to get rid of him. And the Vikings have "a good track record of getting to the truth," he said.

The team said Friday the investigation in under way and the two attorneys heading the probe will interview current and former members of the organization.

HLN's AJ Willingham contributed to this story.