Trump initially wrote on his Truth Social platform, warning Iran that if it "violently kills peaceful protesters", the United States "will come to their rescue".
At least seven people have been killed so far in violence surrounding demonstrations.
"We are locked and loaded and ready to go," Trump wrote on Friday without elaborating.
Shortly after, Ali Larijani, a former parliament speaker who serves as the secretary of Iran's Supreme National Security Council, alleged on the social platform X that Israel and the US were stoking the demonstrations.
He offered no evidence to support the allegation, which Iranian officials have repeatedly made during years of protests sweeping the country.
"Trump should know that intervention by the US in the domestic problem corresponds (to) chaos in the entire region and the destruction of the U.S. interests," Larijani wrote on X, which the Iranian government blocks.
"The people of the US should know that Trump began the adventurism. They should take care of their own soldiers."
Larijani's remarks likely referenced America's wide military footprint in the region.
Iran in June attacked Al Udeid Air Base in Qatar after the US strikes on three nuclear sites.
