"Trump’s claim that they were going to blow up our embassy is the equivalent of a 'weapons of mass destruction' [claim] in the Iraqi war," Deustch said on Friday.
Deutsch added that the media should continue pursuing the issue, rather than letting it fall away from the news cycle.
"We can’t let the 24/7 news cycle take us past that. We should be probing, pushing, 'Where did that come from? Tell us more about that.' Let’s not let today just move on," Deutsch said.
"That was a big statement, that he took out [Quds Force Gen. Qassem] Soleimani based on the fact that they were going to blow up the U.S. Embassy," he continued. "The press needs to chew on that like a bone and not let it go. That is a big, fat lie."
In an interview with Fox News' Laura Ingraham, the president also said he believed that Iran was targeting four American embassies before last wee's drone strike that killed Soleimani.
Rep. Pramila Jayapal, D-Wa., claimed Trump had "recklessly assassinated Qassem Soleimani. He had no evidence of an attack."
Rep. John Rutherford, R-Fla., said on Wednesday that Jayapal was lying.
"I was in the same briefing as you, @RepJayapal, and this is absolutely false. You and your squad of Ayatollah sympathizers are spreading propaganda that divides our nation and strengthens our enemies," he tweeted.
Democrats have warned that Trump's strike could ignite a much larger armed conflict in the Middle East.
The administration claimed that Soleimani was plotting to take American lives in Iraq and killed him in an act of self-defense to de-escalate the conflict.