Ms Omar, who serves as Representative for the state of Minnesota, is Somali-born and is part of a group of congresswomen previously told to "go home" by the President - comments that were widely condemned across the US political spectrum and by world leaders.
Speaking at a campaign rally event in Pennsylvania on Tuesday, Mr Trump said of Ms Omar: "She's telling us how to run our country. How did you do where you came from? How is your country doing?"
In a tweet, the congresswoman responded: "Firstly, this is my country & I am a member of the House that impeached you."
She continued: "Secondly, I fled civil war when I was 8. An 8-year-old doesn’t run a country even though you run our country like one."
The congresswomen then shared a meme from the popular 2004 film Mean Girls asking "why are you so obsessed with me?" and wrote: "These cult-like rallies leave me wondering one thing".
At the rally, President Trump attacked his "radical left" opponents, referring to "AOC plus three".
All four women of colour were elected to the House of Representatives in 2018.
Ms Omar was the target of Trump supporters in July 2019 when a rally in North Carolina repeatedly chanted "send her back" after the President mentioned the congresswoman in his speech.
The President used the event in Pennsylvania on Saturday to round on his Democrat opponent, Joe Biden, in the upcoming election.
"My opponent is against oil, guns and God," Mr Trump said of the Democrat.
Sticking with the issue of energy and the options for renewable sources, the Preisdent said: "Our opponents, they don't want petroleum products, OK? They want wind.
"Let's open up wind. Let's have some wind. And every once in a while, the wind will blow and you'll produce a couple of things," he added.
The President addressed a large crowd with seemingly few social distancing measures in place, though footage from the event does show some supporters wearing 'Make American Great Again' face masks.
President Trump has said the figure is "a shame" but added that, without the actions of his administration, it could have been "much more".