The fourth-generation jet known as “Koswar” has “advanced avionics” and a multi-purpose radar and the Tasnim news agency claims it was “completely indigenously made”.
The “advanced” jet is to be produced in two versions, including a single cabin version as well one with two cabins.
It will be used for aerial support missions as well as for pilots’ training.
Addressing military officials in Tehran, Rouhani said: “We should make ourselves ready to fight against the military powers who want to take over our territory and our resources.
“Why does the United States not attack us? Because of our power, because it knows the consequences.”
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He added that the country’s military power is meant for defence but warned it would retaliate against a hostile move.
Koswar refers to a river in paradise and is a chapter in the Koran.
The unveiling comes a day before Wednesday’s national defence industry day.
Iran lacks a powerful, modern air force and has relied on Russia to provide air power during its intervention in Syria.
It has sent weapons and thousands of soldiers to help President Bashar al-Assad but could only provide a few dozen strike aircraft.
Iran has relied on ageing Russian and US aircraft acquired before the 1979 Iranian revolution.
In 2013, Iran unveiled was it said was a new, domestically built fighter jet called Qaher 313, but experts casted doubt on its viability.
The Islamic Republic has a sizeable domestic arms industry despite international sanctions and embargoes baring it from importing many weapons.
Iran’s new aeroplane comes amid rising tensions between Tehran and Washington.
International sanctions on Iran were lifted when the 2015 nuclear agreement with other major world powers – the UK, France, China, Russia and Germany – came into force the following year.
But Mr Trump pulled out of the agreement in June, labelling the deal struck under the Presidency of Barack Obama as “one of the worst deals ever”.
Tougher measures targeting Iran’s lucrative oil exports – which could plummet by two-thirds by the end of this year – are expected to take effect from November.
Last week, Iran threatened the US with war in a vow of unity with Turkey after Mr Trump imposed further tariff sanctions on the country that has crippled the lira.
Iranian Foreign Minister Javad Zarif warned the US President that the “entire world would unite” and use “force” the US to scrap fresh sanctions imposed as a result of a spat over a detained American pastor and Turkey’s defiance to buy oil from Iran.