A US diocese has apologised and vowed to take action after videos emerged showing boys from a Catholic private school mocking an elderly Native American man at a rally in Washington DC, triggering widespread criticism.

The incident occurred on the steps of the Lincoln Memorial on Friday when the annual anti-abortion March for Life coincided with a rally by indigenous communities calling for their rights to be respected.

In footage captured on multiple phone camera videos that swept social media yesterday, a student from Covington Catholic High School in Kentucky wearing a Make America Great Again hat is seen smirking as he stands extremely close to Nathan Phillips, a Native American Vietnam war veteran, who beats a traditional drum while chanting.

Other teens, many also wearing clothing bearing President Donald Trump's political slogan jeered, jumped and appeared to mock the man.

The Diocese of Covington and Covington Catholic High School issued a statement rebuking the students after their displays drew widespread derision.

"We condemn the actions of the Covington Catholic High School students towards Nathan Phillips specifically, and Native Americans in general, Jan. 18, after the March for Life, in Washington, DC," the statement said.

"We extend our deepest apologies to Mr Phillips. This behaviour is opposed to the Church's teachings on the dignity and respect of the human person. The matter is being investigated and we will take appropriate action, up to and including expulsion."

Kaya Taitano, a witness to the incident, was quoted by CNN as saying Mr Phillips had decided to intervene with a "healing prayer" when the school teens got into a verbal altercation with a group of African American youths who had been preaching about the bible nearby.

An emotional Mr Phillips gave his reaction in a separate video. "I heard them saying, 'Build that wall, build that wall.' We're not supposed to have walls here, we never did.

"I wish I could see that energy of that young mass of young men ... into making this country really, really, great. Helping those that are hungry."

Deb Haaland, one of the first two Native American women elected to Congress in November, linked the students' behaviour to rising levels of racial intolerance under the Trump administration.

"This Veteran put his life on the line for our country," she wrote on Twitter.

"The students' display of blatant hate, disrespect, and intolerance is a signal of how common decency has decayed under this administration. Heartbreaking."