Two other prominent Parkland student activists, Jaclyn Corin and David Hogg, both of them vocal proponents of tighter gun restrictions, are headed to Harvard this fall. Mr. Hogg, who is completing a gap year, garnered attention when he announced his acceptance last year after being rejected from other schools, including from California State University at Long Beach. On Monday, Mr. Kashuv’s defenders noted that Mr. Hogg had a 4.2 grade point average and scored 1270 on the SAT test, while Mr. Kashuv said in the interview that he had a 5.4 G.P.A., and a 1550 SAT score.

Unlike some of his classmates who became national figures after starting a youth movement against gun violence, Mr. Kashuv garnered widespread attention as a young voice in favor of gun rights. In Washington, he lobbied in support of the STOP School Violence Act and a law stepping up requirements for reporting on criminal background checks on gun buyers, both passed in 2018.

He served as the high school outreach director for Turning Point USA, a conservative group with ties to the Trump family. Mr. Kashuv has since stepped down from that position, though he said on Monday his departure was unrelated to the comments that got him into trouble with Harvard.

A video showing screenshots of what he wrote, including repeated racial slurs, was posted online last month by a former schoolmate. The screenshots show that Mr. Kashuv and other students used a Google Doc study guide as a chat, with several of them editing the document simultaneously and commenting on each other’s remarks. In laying out the story Monday morning to his 304,000 Twitter followers, Mr. Kashuv said the “egregious and callous” comments were made “in an attempt to be as extreme and shocking as possible,” not because of any personal beliefs.

One screenshot shows Mr. Kashuv using a racial slur for African-Americans more than a dozen times.

“like im really good at typing” the slur, he wrote. “ok like practice uhhhhhh makes perfect son??!!”

In a different screenshot of a text message, Mr. Kashuv also used the slur to refer to black student athletes.

Ariana Ali, the former schoolmate who posted video of the messages on Twitter, declined to elaborate on Monday beyond praising Harvard’s rescinding of Mr. Kashuv’s admission offer.