The Treasury Department said the move was ordered because the company provides financial support to Khatam al-Anbiya Construction Headquarters, the engineering conglomerate of the Islamic Revolutionary Guard Corps (IRGC).
"Maximum pressure on Iran's regime continues today", Secretary of State Mike Pompeo said, adding that US will continue to act to "deny the regime the money it needs to destabilize the Middle East".
Trump has said that deal was "fatally flawed" because it did not address Iran's ballistic-missile program or Tehran's alleged state sponsorship of terrorism.
"Iran has quadrupled its production of enriched uranium amid tensions with the USA over Tehran's unraveling nuclear accord, two semi-official news agencies reported Monday, an announcement that came just after President Donald Trump and Iran's foreign minister traded threats and taunts", reports the Associated Press.
The Trump administration has broken the multinational agreement on Iran's nuclear industry signed under his predecessor and ramped up economic sanctions against Tehran, re-imposing those lifted under the nuclear deal and issuing more.
On Friday, the United States targeted the Persian Gulf Petrochemical Industries Company (PGPIC) for providing financial support to the economic arm of the IRGC, a military organization in charge of Iran's ballistic missile and nuclear programs.More news: Judges throw out Brexit case against UK PM candidate Johnson
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Tensions have risen between Iran and the United States in recent weeks after Washington sent more military forces to the Middle East, including an aircraft carrier, B-52 bombers and Patriot missiles, in a show of force against what USA officials call Iranian threats to us troops and interests in the region.
Iran has denied responsibility for the May 12 attacks on four tankers off the United Arab Emirates coast.
The move aims to choke off financing to the country's largest and most profitable petrochemical group and extends to its 39 subsidiaries and "foreign-based sales agents", the Treasury Department said in a statement.
That network comprises 40 percent of Iran's petrochemical production capacity, the US Treasury said, and produces half of the country's total petrochemical exports.
However, several analysts said the sanctions' effect will be moderated somewhat because non-U.S. companies already have begun to avoid doing business with Iran's petrochemicals sector because of existing sanctions.
The sanctions come amid escalating tensions with Iran.
Suzanne Maloney of the Brookings Institution think tank described the latest sanctions as "a natural next step in what I think is a deliberately redundant array of restrictions". The new measures follow a round of sanctions imposed last month that targeted the Islamic Republic's export revenues from industrial metals.