(CNN) The US is warning Iran it's taking Tehran's threats seriously and will hold it accountable if it compromises the safety of any American.

The comments came in a tweet from US State Department spokeswoman Morgan Ortagus on Saturday, after Iran announced sanctions against American Mark Dubowitz and his foundation for what it called "US economic terrorism."

"The outlaw regime in Iran issued a threat today against @FDD, an American think tank, and its CEO. The U.S. takes the regime's threats seriously. We intend to hold Iran responsible for directly or indirectly compromising the safety of any American," Ortagus said.

The outlaw regime in Iran issued a threat today against @FDD, an American think tank, and its CEO. The U.S. takes the regime's threats seriously. We intend to hold Iran responsible for directly or indirectly compromising the safety of any American. — Morgan Ortagus (@statedeptspox) August 25, 2019

Iran's Foreign Ministry earlier announced sanctions on the Foundation for Defense of Democracies (FDD) and Dubowitz, its CEO, for "heightening the impact of the US sanctions on the Iranian nation," according to Iran's semi-official Mehr news agency.

Read More