“Following the president’s tweet, I spoke with the sergeant-at-arms to ensure that Capitol Police are conducting a security assessment to safeguard Congresswoman Omar, her family and her staff,” Ms. Pelosi said in a statement. “They will continue to monitor and address the threats she faces.”

After Ms. Pelosi released her statement, a spokesman for Ms. Omar, Jeremy Slevin, said, “Our office has seen an increase in direct threats on Rep. Omar’s life — many directly referencing the president’s video.” He said Ms. Omar’s office has collected a series of menacing tweets over the last few days, some accusing her of treason.

The footage promoted by Mr. Trump intercut images of the World Trade Center aflame with comments from Ms. Omar, one of the first Muslim women elected to Congress, about the treatment of Muslims after Sept. 11. Conservatives have seized on those remarks as dismissive of the attacks.