Rouhani says Iran won't accept any limitations on its missile program, which he says is not part of the landmark nuclear deal reached with world powers in July.
His order to accelerate the program came in a letter to the defense minister, which was posted on the president's website today.
A senior US official told the AP yesterday that America is considering designating a number of additional targets for sanctions related to Iran's ballistic missile program.
The United States has made clear that the missile program is "entirely separate" from the nuclear deal, which is to lift sanctions in return for Iran curbing its nuclear program.