It started when Omar responded to a tweet from Greenwald saying the FBI should investigate Brennan for Logan Act violations. Brennan had condemned the killing of Iranian nuclear scientist Mohsen Fakhrizadeh as "criminal" and "highly reckless" in a Friday tweet.
The law punishes individuals involved in foreign government affairs without permission and is often cited in relation to the 2017 Russia Investigation. Greenwald argued on Twitter that the law is "about undermining current U.S. foreign policy."
Omar responded to Greenwald's comment, saying Brennan's tweet "wouldn’t constitute a violation of the Logan Act" because it was a "one-sided communication and even if directed at a foreign power, seems to fall outside the statute’s scope."
Greenwald -- who recently resigned from the publication he co-founded for alleged "repression, censorship and ideological homogeneity" -- then published a blog post about Omar's response, titled, "Rep. Ilhan Omar’s Misguided Defense of John Brennan and The Logan Act: a Dangerous and Unconstitutional Law."
"Two things I never though[t] I'd see: 1) @IlhanMN defending John Brennan, who bombed and killed civilians in numerous countries including Somalia, and 2) @IlhanMN defending an old, repressive law designed to criminalize dissent from US Foreign Policy. Welcome to Trump-era politics," Greenwald tweeted in a thread linking back to the blog post.
Omar called Greenwald's tweet "a weird assertion" and "ludicrous."
"...At no point did I provide a defense for either," she said. "This is simply ludicrous, but I am sure you knew that."
Greenwald argued that the Minnesota congresswoman "absolutely did" defend Brennan and the act.
"The principal argument against the Logan Act for decades is that it's so vague nobody knows what it includes, leaving it to FBI to unilaterally threaten dissidents. You claimed it has clear definitional contours & know what it encompasses. That's a defense," he tweeted.
Omar called his argument "wrong" and went on to defend her tweet about the Logan Act as "a factual limitation of a law" and accused Greenwald of having "personal feelings wrapped up" in their debate.
The Logan Act is an obscure statute that has never been successfully used in a criminal prosecution and was intended to prevent individuals from claiming falsely to represent the United States government abroad.
Fox News' Brook Singman contributed to this report.