Cruz was responding to a tweet in which Omar called on members of Congress to step in and prevent President Trump from engaging in armed conflict with Iran.
Cruz tweeted: "According the the [sic] Obama Department of Defense, Qasem Soleimani was a terrorist directly responsible for the murder of over 500 US service men [sic] & women. Why are congressional Dems outraged that he’s finally dead?"
In response, Omar suggested that Cruz was purposefully overlooking the actual nature of her criticism.
"We are outraged the president would assassinate a foreign official, possibly setting off another war without Congressional authorization and has zero plan to deal with the consequences," she responded. "But of course you know that."
She also tweeted a quote in which Cruz, President Trump's former opponent in the 2016 Republican primaries, cast doubt on Trump's ability to lead.
Omar also criticized Trump, indicating that he was doing what he predicted former President Obama would do with Iran: start a war.
"This reckless mind is now leading us to war!" she tweeted, alongside screenshots of Trump's previous tweets.
Both Cruz and Omar sit on the Senate and House foreign relations committees, respectively. While it's unclear how Congress will proceed, the president would need the legislative branch's approval for a formal declaration of war.
Cruz also defended Trump from rhetorical attacks by former Obama administration official Ben Rhodes.
"Trump may have just started a war with no congressional debate," Rhodes tweeted.
Cruz responded by mocking the Iranian nuclear deal set up under Rhodes and the former president., tweeting: "Perhaps it would have been a better idea to send him $1.7 billion in unmarked bills, in pallets on planes in the dead of night, so he could kill more Americans?"