Rouhani was speaking at a military parade where an Iranian news agency said one of the weapons on display was a new ballistic missile with range of 2,000 km (1,200 miles), capable of carrying several warheads.
Iran on Friday unveiled a new long-range ballistic missile as the country marked the beginning of Defence Week.
The unveiling occurred during a parade held to celebrate the 1980s Iraq-Iran war.
Friday's parade also showcased various Iranian army units and Revolutionary Guard forces, as well as the police.
The move was a direct challenge to President Trump, who in August signed a bill imposing mandatory penalties on those involved in Iran's ballistic missile program and anyone who does business them.
"The missile has become smaller in size (compared to other Iranian ballistic missiles) and more tactical, and it will be operational in the near future", Hajizadeh said without further elaboration.
Rouhani described the USA and Israel as the main destabilizing forces in the Middle East and said the speech by Trump and a later address by Israeli Prime Minister Benjamin Netanyahu were a "clear indicator of the vicious nature" of the two countries, according to the Tasnim news agency.
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Tehran has backed Yemen's Shiite rebels known as Houthis against a US -supported and Saudi-led coalition of mostly Arab states that seeks to return the internationally elected government to power in Yemen.
U.S. Secretary of State Rex Tillerson has said that the agreement must be changed or the United States could not stick with it. Iran has said its nuclear accord cannot be renegotiated.
He also criticized remarks from Israeli Prime Minister Benjamin Netanyahu, saying the United States and Israel have isolated themselves from global opinion in their opposition to the Obama-era agreement - which limits Tehran's nuclear activities to the laboratory in exchange for lifting USA -imposed economic sanctions.
Trump called on world powers to pressure Iran to stop developing missiles and cease supporting regional militant groups.
Later on Friday, Iranians staged anti-Trump protest to show their anger over the US president's speech. Thousands of worshipers marched after Friday prayers in Tehran, chanting "Death to America" and "Death to Israel".
State media said similar protests took place in other Iranian cities and towns.
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