A writer for NBC’s “Saturday Night Live” apologized Monday for a tweet targeting 10-year-old Barron Trump, son of President Donald J. Trump, after being suspended from the show.

Katie Rich, 33, was suspended immediately after her Friday tweet and the suspension is indefinite, according to a source familiar with the situation.

Ms. Rich, who posted an Inauguration Day tweet saying that “Barron will be this country’s first homeschool shooter,” initially took down her Twitter page amid a firestorm of criticism, but then reactivated the account Monday in order to post a public apology.

“I sincerely apologize for the insensitive tweet,” said Ms. Rich. “I deeply regret my actions & offensive words. It was inexcusable & I’m so sorry.”

The Friday tweet prompted a rash of online petitions calling for NBCUniversal to fire Ms. Rich, a writer for “Saturday Night Live” since December 2013, for picking on the youngest of the president’s five children.

“Online bullying of children (including and especially those in our White House!) by any adult is unacceptable behavior and should not be tolerated under any circumstances,” said a Change.org petition that had collected more than 38,000 signatures as of Monday.

“If Ms. Rich does not get fired, heftily fined AND issue a written apology to our First Family immediately, NBC should be banned from our White House press room and shunned by our new administration, and SNL should be boycotted into oblivion,” said the petition.

Ms. Rich removed the Friday tweet about three hours after posting it, but screen shots circulating online drew condemnation throughout the weekend.

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