The statement on Friday said Trump is willing to take new measures “unless all unjustly imprisoned American citizens are released and returned”, reports Voice of America news.
The President’s remarks come after a Chinese American, Xiyue Wang, was sentenced in Iran this week to 10 years in prison over espionage charges.
“The US condemns hostage takers and nations that continue to take hostages and detain our citizens without just cause or due process,” the statement said.
The statement urged the release of Robert Levinson, an American former law enforcement officer who disappeared more than 10 years ago in Iran; and US businessman Siamak Namazi and his father, Baquer.
“Iran is responsible for the care and well being of every US citizen in its custody,” the Voice of America quoted the statement as saying.
On Tuesday, the Trump administration put new economic sanctions against Iran over its ballistic missile programme and said Tehran’s “malign activities” in the Middle East undercut any “positive contributions” coming from the 2015 nuclear agreement.
Trump has called the agreement “the worst deal ever negotiated”.