The US President, speaking in the Oval Office, said he “disagreed” with the statement and “felt a little bit badly” about it.
The controversial incident took place at Mr Trump's campaign rally in North Carolina earlier this week.
"I was not happy with it. I disagree with it," Mr Trump said after he was asked why he did not stop his supporters.
"It was quite a chant and I felt a little bit badly about it.”
Mr Trump said he started speaking quickly to drown the chants out, though video showed him not speaking for more than 10 seconds after the crowd started shouting.
"I started speaking very quickly but it started up rather fast, as you probably noticed."
Ilhan Omar is a US citizen who emigrated from Somalia with her family after fleeing the country's civil war.
She has labelled the president “fascist”.
She added: “This is what this president and his supporters have turned our country into.”
The Congresswoman was greeted by cheering supporters chanting “welcome home, Ilhan” in Minnesota this week.
A political storm over race has been unleashed in the US in the past week, following tweets from the President.
....and viciously telling the people of the United States, the greatest and most powerful Nation on earth, how our government is to be run. Why don’t they go back and help fix the totally broken and crime infested places from which they came. Then come back and show us how....— Donald J. Trump (@realDonaldTrump) July 14, 2019
Ms Omar is one of a group of four Democrat Congresswomen who the president has attacked in the past week.
President Trump has accused Ms Omar, Alexandria Ocasio-Cortez, Rashia Tlaib, and Ayanna Pressley - known collectively as "the Squad" - of hating America.
Earlier in the week, the President tweeted that the four could “go back” to their countries “from which they came”.
Other than Ms Omar, all the three other women were born in the US.
All four are US citizens.
He has also spoken to reporters about rumours that Ms Omar was married “to her brother” but added that “I know nothing about it”.
The President’s “go back” Twitter rant was declared racist by the US Congress.
Earlier this week, a bid to launch impeachment proceedings against Mr Trump was blocked in the House of Representatives.