Her statement late Sunday followed an announcement by House Speaker Nancy Pelosi that she has taken steps to ensure the safety of the Minnesota Democrat and the speaker's call for Trump to take down the video.
Pelosi was among Democrats who had criticized Trump over the tweet, with some accusing him of trying to incite violence against the Muslim lawmaker. An upstate New York man recently was charged with making death threats against her.
White House press secretary Sarah Sanders defended Trump earlier Sunday, saying the president has a duty to highlight Omar's history of making comments that others deem anti-Semitic or otherwise offensive and that he wished no "ill will" upon the first-term lawmaker.
But Omar said that since Trump retweeted the video Friday night, she's received many threats on her life that referred or replied to the posted video.
"Violent crimes and other acts of hate by right-wing extremists and white nationalists are on the rise in this country and around the world," she said. "We can no longer ignore that they are being encouraged by the occupant of the highest office in the land." She said: "We are all Americans."
Earlier, Pelosi issued a statement while traveling in London saying she had spoken with congressional authorities "to ensure that Capitol Police are conducting a security assessment to safeguard Congresswoman Omar, her family and her staff."
Pelosi said officials will continue to monitor and assess threats against Omar, and called on Trump to discourage such behavior.
"The President's words weigh a ton, and his hateful and inflammatory rhetoric creates real danger," Pelosi said. "President Trump must take down his disrespectful and dangerous video."
The video in Trump's tweet included a snippet from a recent speech Omar gave to the Council on American-Islamic Relations, in which she described the Sept. 11, 2001, terrorist attack on the World Trade Center as "some people did something," along with news footage of the hijacked airplanes hitting the Twin Towers. Trump captioned his tweet with: "WE WILL NEVER FORGET!"
Neither Trump's tweet nor the video included Omar's full quote or the context of her comments, which were about Muslims feeling that their civil liberties had eroded after the attacks. The tweet was posted atop Trump's Twitter feed for much of Sunday, with more than 9 million views. It remained lower in the feed after Pelosi requested that the video be pulled.
Sanders questioned why Democrats weren't following Trump's example and calling out Omar, too. Democrats who criticized the president over the tweet defended Omar, with some noting their past disagreements with her.
"Certainly the president is wishing no ill will and certainly not violence towards anyone, but the president is absolutely and should be calling out the congresswoman for her — not only one time — but history of anti-Semitic comments," Sanders said. "The bigger question is why aren't Democrats doing the same thing? It's absolutely abhorrent the comments that she continues to make and has made and they look the other way."
Omar repeatedly has pushed fellow Democrats into uncomfortable territory with comments about Israel and the strength of the Jewish state's influence in Washington. She apologized for suggesting that lawmakers support Israel for pay and said she isn't criticizing Jews. But she refused to take back a tweet in which she suggested American supporters of Israel "pledge allegiance" to a foreign country.
Rep. Jerry Nadler, a New York Democrat who represents Manhattan's financial district, which was targeted on 9/11, said he had no issues with Omar's characterization of the attack.
"I have had some problems with some of her other remarks, but not — but not with that one," he said.
Sanders commented on "Fox News Sunday" and ABC's "This Week." Nadler appeared on CNN's "State of the Union.
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