The remark came nearly a week after the president tweeted that Omar and three other members of “the Squad” should “go back and help fix the totally broken and crime infested places from which they came.
"Then come back and show us how it is done," the president added.
Trump also defended his supporters at last week's North Carolina rally who chanted “Send her back!” in reference to Omar -- something that, along with the tweets, was viewed by most Democrats and some Republicans as racially insensitive.
"Those are incredible patriots,” Trump told reporters, referring to the Wednesday crowd in Greenville, N.C. “But I’m unhappy when a congresswoman goes and says, 'I’m going to be the president’s nightmare.'
"She’s going to be the president’s nightmare? She’s lucky to be where she is, let me tell you. And the things that she has said are a disgrace to our country.”
Omar came to the United States as a Somali refugee when she was a teen and is a naturalized U.S. citizen.
On Friday morning, Trump tweeted that the “fake news media” had become “crazed” over the “Send her back!” chant and asserted that a gathering of supporters greeting Omar at a Minnesota airport last week had been “staged.”
On Saturday, an Omar ally, Rep. Alexandria Ocasio-Cortez, D-N.Y., defended her fellow Democrat, claiming Trump had "relished' in the anti-Omar chanting at the rally.
"He kind of presided over the situation, he relished it, he took it in," Ocasio-Cortez said at a town hall on immigration in her New York City district.
When a reporter asked her whether she believed Trump had led the crowd on, Ocasio-Cortez replied: "He absolutely did."
Fox News' Sam Dorman contributed to this story.