Ms Omar blasted the false smear, saying the tweet had put her life at risk.
The young Muslim congresswoman — who has been branded a member of Alexandria Ocasio-Cortez's "squad" — has frequently been targeted by the President.
In July, he suggested she had married her own brother to commit immigration fraud — a baseless claim based on a single, anonymous message-board post.
Social media users quickly pointed out that the video had been taken on Friday, two days after the anniversary, while Omar was attending events related to the Congressional Black Caucus Foundation Legislative Conference in Washington.
Others called for Twitter to remove the tweet or suspend Williams' account. Hours after Trump retweeted Williams' video, the original tweet was removed.
The video was deleted by the user, and Twitter did not take action on the tweet, the tech company said in an email. The President's tweet remains live, although without the video, and users have continued to respond.
Mr Trump has used his Twitter account to spread misinformation from Williams before. In August, the President shared another one of Williams' videos, which disputed, without evidence, that the late financier Jeffrey Epstein committed suicide while in federal custody.