Clinton, apparently taken aback by the accusations flung at her, can be seen apologizing profusely for what she argues was an unintended offense.
A friend of one of the activists posted a short video of the altercation on Twitter.
Omar, who invited Clinton to talk about the issue. "I look forward to building an inclusive movement for justice with you", she added.
"And I want you to know that and I want you to feel that deeply - 49 people died because of the rhetoric you put out there".
I do believe words matter.
"I'm so sorry", Clinton is heard saying on the video, "it certainly was never my intention, I do believe words matter, I believe we have to show solidarity".
"What does "I'm sorry you feel that way" mean?" another student asked. "What does that mean?" demanded another activist.
"T$3 he CAUCASITY that chelsea clinton has showing up to a vigil for the 49 muslims massacred in an islamophobic hate crime after STOKING ISLAMOPHOBIA AND RACISM surrounding ilhan omar. f**king ridiculous", she tweeted.
Like many other Democrats and Republicans, Clinton distanced herself from the comments.
The clip immediately went viral and while the person who originally posted then deleted her Twitter account following a backlash, the footage is still available online. "There is no sense of responsibility".
Some of the NYU students told Clinton she wasn't welcome at the vigil. The Somali-American congresswoman, one of the two Muslim Americans in the federal legislature, was accused of invoking an anti-Semitic trope and implying that American Jews might have dual allegiance.
Clinton was among establishment Democrats who tore into Omar for her suggestion that the wealthy Israeli lobby has an overbearing influence in United States politics.