What Mr. Trump Said

“She smeared U.S. service members involved in Black Hawk Down, in other words, she slandered the brave Americans who were trying to keep peace in Somalia.”

“Black Hawk Down” refers to a 17-hour firefight on Oct. 3, 1993, that broke out between American forces and Somali militiamen in Mogadishu during the country’s civil war. Ms. Omar and her family fled Somalia during that war.

In 2017, Ms. Omar wrote, “thousands of Somalis killed by American forces that day!”

Her figure is a matter of dispute, but whether her comment amounted to a “smear” or “slander” is a matter of opinion.

American forces deployed to Somalia in 1992 as part of a humanitarian effort. Their mission culminated the next year when forces aligned with the warlord Muhammad Farah Aideed shot down two Black Hawk helicopters in a battle in which 18 Americans were killed and 75 wounded. The events were depicted in the book “Black Hawk Down” by the journalist Mark Bowden and a film of the same name.

The army has cited estimates of between 500 and 1,700 Somali casualties. Mr. Bowden reported that most death toll estimates ranged from 300 to 500 Somalis. Robert Oakley, the ambassador to Somalia under President George Bush, said in a 1998 interview that he believed between 1,500 to 2,000 Somalis were killed and wounded.

What Mr. Trump Said

“She pleaded for compassion for ISIS recruits attempting to join the terrorist organization.”

Ms. Omar wrote a letter to a federal judge asking for leniency in sentencing on behalf of nine Somali-American men, who were found guilty or pleaded guilty in 2016 to charges that they tried to travel to Syria to join the Islamic State.

“I bring to your attention the ramifications of sentencing young men who made a consequential mistake to decades in federal prison. Incarcerating 20-year-old men for 30 or 40 years, is essentially a life sentence,” Ms. Omar wrote in November 2016. “Such punitive measures not only lack efficacy they inevitability create an environment in which extremism can flourish, aligning with the presupposition of a terrorist recruitment: ‘Americans do not accept you and continue to trivialize your value. Instead of being a nobody, be a martyr.’”

“The best deterrent to fanaticism is a system of compassion,” the letter continued.

What Mr. Trump Said

“Omar laughed that Americans speak of Al Qaeda in a menacing tone and remarked that you don’t say America with this intensity, you say Al Qaeda. It makes you proud. Al Qaeda makes you proud. You don’t speak that way about America.”

Mr. Trump distorted Ms. Omar’s remarks. In that 2013 local news interview, Ms. Omar was discussing the rhetoric around terrorism. When the host noted that “we keep the Arabic names” of terrorist groups, she responded with an anecdote about a college professor who would say the names with “intensity, so it must mean or hold a bigger meaning.”