Rouhani addressed the parade in Tehran, saying that Iran would not halt its missile program but continue to boost military capabilities, despite US demands.
USA defense officials said the test seemed to be a failure because the missile crashed or exploded after flying more than 500 miles.
The state-run IRNA news agency quoted chief of the Guard's airspace division, Gen. Amir Ali Hajizadeh, as saying that the ballistic missile "can carry several warheads for various uses".
"We will increase our military power as a deterrent".
Iran says all of its missiles are created to carry conventional warheads only and has limited their range to a maximum of 2,000 kilometers, although commanders say they have the technology to go further.
"Extremely concerned by reports of Iran missile test, which is inconsistent with United Nations resolution 2231".
Israel's Defence Minister Avigdor Lieberman on Saturday denounced Iran's testing of a medium-range missile as a "provocation" and said it was proof of Tehran's ambition to become a world power. Iran says it has no such plans.
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The range of this missile would cover most of the Middle East, including Israel. "We seek no one's permission to defend our land".
Iran already has two other missiles, Ghadr-F and Sejil, capable of reaching Israel, the sworn enemy of Iran, and the us bases located in the region.
"The ballistic missile will be operational in the near future".
He also criticized the 2015 pact that the United States and six other powers struck with Iran under which Tehran agreed to restrict its nuclear program in return for relief from economic sanctions.
Later on Friday, Iranians staged anti-Trump protest to show their anger over the US president's speech.
Trump has singled out the Joint Comprehensive Plan of Action (JCPOA), popularly called the 2015 Iran Nuclear Deal, for disdain, and has repeatedly flirted with voiding the landmark agreement.
Global experts are nearly unanimous in their opinion that Iran is abiding by the pact that saw Tehran agree to limit its nuclear program, which the West believed was aimed at developing weapons, in exchange for the easing of worldwide economic sanctions.
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