His executive order threatens top officials on the International Criminal Court with economic penalties for looking into potential U.S. war crimes.
The investigation will target the Taliban, Afghan forces and U.S. military and intelligence personnel.
The president's threat to target cultural sites was in keeping with his longstanding disregard for international law.
Destroying cultural property during armed conflict is considered a war crime under international law, one the U.S. has decried in the past.
"This is a war crime," Rep. Alexandria Ocasio-Cortez tweeted to Trump after he threatened to destroy Iranian cultural sites. "It makes you a monster."
The president, at his campaign rally in Sunrise, Florida, talked about his pardons of three men accused of war crimes, whom he called "great fighters."
Richard Spencer, who resigned as Navy secretary, defended his attempt to continue disciplinary proceedings against convicted war criminal Eddie Gallagher.
The 2020 Democratic presidential contender said she wants to stop politicians from “fighting in these wasteful regime-change wars."
The president has repeatedly sided with Navy SEAL Edward Gallagher, who was acquitted of war crimes last month.
Trump is considering pardoning Gallagher, who faces trial for murdering an Islamic State prisoner in his care and attempting to murder civilians.