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(CNN) —  

The White House has reached out to Covington Catholic High School students after video of an encounter between students from the school and Omaha Nation elder Nathan Phillips stirred a national debate.

“We’ve reached out and voiced our support” for the students, White House press secretary Sarah Sanders told reporters Tuesday evening.

She continued, “Certainly no one understands better than this President when the media jumps to conclusions and attacks you for something you may or may not have done.”

The Covington Catholic High School students were criticized when a brief video surfaced on Friday showing them wearing Make America Great Again hats and mocking Phillips during the school’s annual trip to a March for Life rally in Washington.

A second video surfaced on Sunday showing another group, who identify themselves as members of the Hebrew Israelites, taunting students with disparaging and vulgar language before the encounter with the Native American.

In an interview to air Wednesday on NBC’s “Today,” a student in the video, Nick Sandmann, indicated he’s open to speaking to Phillips, and Phillips has offered to travel to the Kentucky high school to talk about the importance of respecting diverse cultures, according to a statement from the Lakota People’s Law Project.

“My position is that I was not disrespectful to Mr. Phillips,” Sandmann told NBC. “I respect him. I’d like to talk to him.”

Sandmann previously denied negative characterizations of his behavior and that of his classmates.

“In hindsight, I wish we could have walked away and avoided the whole thing,” he said.

It’s unclear if or when a White House visit would take place, per Sanders, due to the partial government shutdown, now in its 32nd day.

“If the President does have them here, it’ll be sometime after the shutdown if that happens,” she said.

CNN’s Darran Simon, Amanda Watts and Eric Levenson contributed to this report.