The new penalties represent the "highest sanctions ever imposed on a country," Trump said.
The president also said that the latest sanctions against Iran go "directly to the top."
US Treasury Secretary Steven Mnuchin, in turn, said the bank was "the last source of funds" for the Iranian authorities.
For its part, Moscow described as illegitimate the new sanctions imposed by the US against the National Bank of Iran.
"We consider unilateral sanctions illegitimate," the director of the Second Asian Department of the Russian Foreign Ministry, Zamir Kabúlov, told Sputnik.
The diplomat said that US actions will not influence cooperation between Russia and Iran in the banking sector.
The National Bank of Iran is the largest financial and commercial institution in the country whose assets were estimated at $ 80 billion in 2016.
In July 2015, Iran and six international mediators – Russia, the United States, the United Kingdom, China, France and Germany – signed the so-called Joint Comprehensive Action Plan (PAIC), which established a series of limitations to the Iranian nuclear program with the aim of excluding its possible military dimension, in exchange for the lifting of international sanctions.
Although the International Atomic Energy Agency (IAEA) confirmed that Tehran complied with the treaty, the US abandoned it in May 2018 accusing Iran of continuing to develop nuclear weapons, and since then re-established several batteries of sanctions against the Islamic Republic.
One year after the US withdrawal from the nuclear pact, Iran suspended part of its commitments under the PAIC.
In particular, it exceeded the reserves of 300 kilos of enriched uranium up to 3.67%, began to enrich it above this limit and announced that it will continue to reduce its obligations progressively every 60 days, unless other signatories of the agreement find a diplomatic solution for bypass U.S. sanctions.