"This is a war crime," said Alexandria Ocasio-Cortez.
President Trump has said the US is "targeting" 52 Iranian sites and will strike "very fast and very hard" if the US or any US assets are attacked.
Trump's remarks follow the US assassination of Qasem Soleimani, a top Iranian general, in a drone strike. The attack also killed Iraqi militia leader Abu Mahdi al-Muhandis.
The US president added that the 52 targets represent the 52 Americans who were held hostage in Iran for 444 days after being seized at the US embassy in Tehran in November 1979.
Soleimani's killing has marked a major escalation of tensions between the two nations and Iran has vowed to take "severe revenge."
In a series of messages that were posted on Twitter, Trump accused Iran of "talking very boldly about targeting certain USA assets."
He also said the US has identified 52 Iranian sites, some "at a very high level & important to Iran & the Iranian culture."
The impeached president did not identify the sites. The Pentagon referred questions about the matter to the White House.
The International Criminal Court - which the US is not a member of - has previously said that intentionally directing attacks against buildings dedicated to religion, education, art, science, charitable purposes or historic monuments is a war crime.
Under the Geneva Convention, it's prohibited to target monuments or places of worship which constitute the "cultural or spiritual heritage of peoples."
The deliberate targeting and destruction of cultural and religious landmarks is also prohibited by the 1954 Hague Convention for the Protection of Cultural Property in the Event of Armed Conflict, by which the U.S. is bound.
Alexandria Ocasio-Cortez and Democratic presidential contender Elizabeth Warren both said that Trump's decisions to target Iranian cultural sites is a threat to commit war crimes.
Trump's tweets followed a funeral procession for General Soleimani held in Baghdad. Mourners waved Iraqi and militia flags and chanted "death to America" and "America is the enemy of God."
https://twitter.com/realDonaldTrump/status/1213593965838163968
https://twitter.com/realDonaldTrump/status/1213593975732527112
https://twitter.com/AOC/status/1213654724282593280
https://twitter.com/ewarren/status/1213665218020171777
Shortly after Trump's tweets were posted, the website of the Federal Depository Library Program, a little-known US government agency, was hacked by a group claiming to be linked to Iran, who posted graphics displaying the Iranian flag and vowed revenge for General Soleimani's death.
A message on the American Federal Depository Library Programme site read: "This is a message from the Islamic Republic of Iran.
"We will not stop supporting our friends in the region: the oppressed people of Palestine, the oppressed people of Yemen, the people and the Syrian government, the people and government of Iraq, the oppressed people of Bahrain, the true Mujahideen resistance in Lebanon and Palestine, [they] will always be supported by us."
The web page contained a doctored image of President Trump, depicting him being hit in the face and bleeding at the mouth.
On Saturday evening, a rocket fell inside Baghdad’s heavily fortified Green Zone near the US embassy, another hit the nearby Jadriya neighbourhood and two more rockets were fired at the al-Balad air base north of the city, but no one was killed.
