Trump tweeted that new sanctions against Iran would be imposed on 24 June.
"We are putting major additional Sanctions on Iran on Monday. I look forward to the day that Sanctions come off Iran, and they become a productive and prosperous nation again," he tweeted.
The US president again criticized what he described as the "terrible Obama plan", referring to the 2015 Joint Comprehensive Plan of Action (JCPOA), also known as the Iran nuclear deal.
On Saturday, Trump dubbed his plan of action "Let's make Iran great again," while speaking to reporters outside the White House.
Tensions between the US and Iran escalated following Thursday's downing of a US spy drone that Iran claimed was operating it its airspace.
US Air Force CENTCOM Commander Joseph Guastella told reporters on Thursday that Tehran's claims regarding an American RQ-4 drone were wrong, and asserted that the unmanned aircraft did not violate Iran airspace.
IRGC Commander-in-Chief Major General Hossein Salami said on Thursday that the downing of the drone was a "clear message" to Washington that Tehran would "react strongly" to any aggression.
CENTCOM claimed that the downing of the drone was an attempt to disrupt the ability of the US to monitor the region following recent threats to international shipping and the free flow of commerce.