Trump put Iran "on notice" in February for test-firing a ballistic missile and imposed new economic sanctions in July over its missile program and "malign activities" in the Middle East. They are also working with North Korea.
Trump has vowed repeatedly to take a tougher line toward Iran than his predecessor, threatening at various times to renegotiate or even dismantle the nuclear deal, and shoot Iranian boats out of the water if they provoke USA naval vessels in the Persian Gulf.
Trump told the UN General Assembly on Tuesday that Iran was building its missile capability and accused it of exporting violence to Yemen, Syria and other parts of the Middle East.
British Foreign Secretary Boris Johnson wrote on Twitter: "Extremely concerned by reports of Iran missile test, which is inconsistent with United Nations resolution 2231". Iran unveiled a new missile with a range of 2,000 kilometres.
The Iranian president reiterated his despise to recent US and Israel stances against the Islamic republic in the UN General Assembly.
Israeli Defence Minister Avigdor Liberman denounced the test as a "provocation" aimed at the United States and its allies, including the Jewish state.
Notably, both China and Russian Federation - from which North Korea drew moral and material support in the past - are advising caution to Kim Jong-un but with little effect.
He said his country would "not be the first" to violate the deal, which Mr Trump has threatened to pull out of. Call on Iran to halt provocative acts'.
In a speech broadcast on state television, Rouhani said: "We will increase our military power as a deterrent".
Tehran has argued that the missile is exclusively for defensive purposes and is not a menace for any country in the region.
That makes them only medium-range but still sufficient to reach Israel or United States bases in the Gulf. "Iran is sending another signal of defiance taken straight from the North Korean textbook", BBC analyst Kasra Naji says.
"The regime has engaged in such launches repeatedly, including in July of this year when it launched a rocket into space that intelligence experts say can be used to develop intercontinental ballistic missile technology", Haley said in a speech at the American Enterprise Institute on September 5.