Trump made the comments after retweeting several accounts criticising House Speaker Nancy Pelosi.
While Esper said he agreed with Trump that additional attacks against United States embassies were likely, he said on CBS's "Face the Nation" that Trump's remarks to Fox News were not based on specific evidence on an attack on four embassies.
The president's political opponents have blasted him for ordering the drone strike against Iranian Gen. Qassem Soleimani, who has been linked to numerous attacks on American forces and more.
Democrats and a few Republicans in Congress have questioned the justification of the attacks and said they have not been given adequate, detailed briefings.
Trump later summed up his views on the matter, stating, "The Democrats and the Fake News are trying to make terrorist Soleimani into a wonderful guy, only because I did what should have been done for 20 years". "The president didn't cite a specific piece of evidence", Reuters quoted Esper as saying.
"I didn't see one with regard to four embassies", Esper answered.
Qasem Soleimani, commander of the Islamic Revolutionary Guard Corp's Quds Force, died in Baghdad on January 3 when the vehicle he was traveling in was struck by a missile launched by a USA drone.
The House of Representatives and the Senate received separate briefings last week about the administration's decision to kill Soleimani.
The Iranian government will seek to prosecute US President Donald Trump for the assassination of Maj.
Republican Senator Mike Lee on Sunday said he was anxious about the integrity of information the president and security briefers have provided Congress about Iran. Congress has the power to declare war while the president, as commander-in-chief, has the power to use the military to defend the US.