One 11-minute video of the confrontation shows a roughly performed dance that doesn't bear much resemblance to a traditional haka, and students loudly chanting before Nathan Phillips and Frejo approached them.
Some viewers of the video have suggested it may have been a school dance as opposed to the haka.
Videos circulating online show a youth staring at and standing extremely close to Phillips, a 64-year-old Native American man singing and playing a drum. Other students, some wearing Covington clothing and many wearing "Make America Great Again" hats and sweat shirts, surrounded them, chanting, laughing and jeering.
The Indigenous Peoples March in Washington coincided with the March for Life, which drew thousands of anti-abortion protesters, including a group from Covington Catholic High School in Park Hills, Kentucky.
In a joint statement, the Roman Catholic Diocese of Covington and Covington Catholic High School apologised and said they are investigating and will take "appropriate action, up to and including expulsion".
"We extend our deepest apologies to Mr Phillips," the diocese statement read. "This behaviour is opposed to the Church's teachings on the dignity and respect of the human person."
According to the "Indian Country Today" website, Phillips is an Omaha elder and Vietnam veteran who holds an annual ceremony honouring Native American veterans at Arlington National Cemetery.
Frejo said he joined Phillips to defuse the situation, singing the anthem from the American Indian Movement with both men beating out the tempo on hand drums.
Although he feared a mob mentality that could turn ugly, Frejo said he was at peace singing despite the scorn. He briefly felt something special happen as they repeatedly sang the tune.
"They went from mocking us and laughing at us to singing with us. I heard it three times," Frejo said. "That spirit moved through us, that drum, and it slowly started to move through some of those youths."
Eventually a calm fell over the group of students and they broke up and walked away.
The videos prompted a torrent of outrage online. Actress and activist Alyssa Milano tweeted that the footage "brought me to tears", while actor Chris Evans tweeted that the students' actions were "appalling" and "shameful".
Covington Catholic High School's Facebook page was not available at time of reporting and its Twitter feed was set to private.
- AP