The United Nations' top court, the International Court of Justice (ICJ), says anything that has an impact on humanitarian aid and civil aviation safety must be suspended.
"I'm announcing that the United States is terminating the 1955 Treaty of Amity with Iran", Pompeo said during a briefing announcing the termination of the agreement.
"The Islamic Republic of Iran's Foreign Ministry sees eye to eye with the International Court of Justice with regards to its ruling, and the tribunal regards itself as having the preliminary competence to look into Iran's lawsuit against the US and, hence, has foiled efforts by the USA government and its lawyers to dismiss the court's competence and shirk its legal responsibilities".
The treaty established economic relations and consular rights and was signed during the terms of former US President Dwight Eisenhower and former Iranian Prime Minister Hossein Ala.
He stressed that Iran is exploiting the International Court of Justice for political purposes.
Iran took the USA to the ICJ twice; first in 1988 over the downing of Iran Air flight 655 and the killing of all 290 people on board and in 1992 in relations to United States attacks on Iranian oil rigs in 1987 and 1988.
Iran alleges that the sanctions imposed by the Trump administration after its withdrawal from a 2015 nuclear deal with Iran violated the so-called Treaty of Amity.
The court ruling was a moral victory for Tehran, even though it was hoping for a more sweeping decision on the US withdrawal from the nuclear deal.
The U.S. and Iran severed diplomatic ties following Iran's 1979 revolution, but the treaty remained in effect.
"Iran is the origin of the current threat to Americans in Iraq", Pompeo told reporters at the State Department.
Iran hawks in the Trump Administration, like Pompeo and National Security Adviser John Bolton, have condemned Iran's continued pursuit of ballistic missile technology and support of proxy militias in war-torn places such as Iraq, Syria, and Yemen.
Last month, Bolton said that the 2,200 USA troops inside Syria are "not going to leave as long as Iranian troops are outside Iranian borders, and that includes Iranian proxies and militias".
Pompeo said Iran has been ignoring the treaty for "an awfully long time", and Washington "ought to have pulled out of it decades ago".
"The United States will not sit idly by as baseless politicized claims are brought against us", Bolton said. Though U.S. military officials have said protesters in the city unhappy over shortages may have been responsible, Pompeo said Iran was behind both the Basra incident and a mortar attack near the U.S. Embassy in Baghdad in early September.
Washington however forcefully told the court - which rules on disputes between United Nations member states - that it has no jurisdiction to rule on this case as it concerns a matter of national security.
In his speech before the United Nations General Assembly last week, President Donald Trump called on all countries to isolate Iran and stop the flow of money to the regime of President Hassan Rouhani.