"At the moment it's not easy to quantify the possible economic impact of the USA withdrawal on European business activities", said the head of the EU's business lobby, Emma Marcegaglia, who called for "legal clarity".
Mnuchin said the U.S.'s goal is to push Iran to re-negotiate the nuclear deal.
Iran said it had asked Europe's Airbus to announce whether it would go ahead with a plane deal with Tehran following the US pullout. The EU has vowed to protect its companies, and could even pursue trade retaliation if the U.S. Treasury moves to penalize European companies.
Iranian politicians held an impromptu demonstration in the country's parliament on Wednesday after U.S. President Donald Trump announced he would be withdrawing from the Joint Comprehensive Plan of Action (JCPOA), the Washington Post reported.
Trump declared Tuesday that the United States is pulling out of the 2015 agreement with Iran, regarding that nation's nuclear weapons program.
US President Donald Trump announced on May 8 that the US was withdrawing from the Joint Comprehensive Plan of Action (JCPOA), an global agreement reached in 2015 by Iran, the United States, Russia, France, China, Great Britain, Germany and the EU.
JCPOA provided for Iran curbing its nuclear programme in return for the lifting of financial sanctions.
The investors are anxious that renewed sanctions against Iran, a major oil producer, could lead to supply disruptions.
Certain waivers can be negotiated, but the US did not say what goods or countries might qualify.
Daily July Brent Crude
Weekly U.S. crude oil production hit another record last week, climbing to 10.7 million barrels per day (bpd).
Oil extended gains above $71/bbl on the risk of supply disruptions as a conflict between Israel and Iran ratcheted up, and after the US renewed sanctions on OPEC's third-largest producer.
Speculators are driving the momentum which is pushing WTI and Brent crude oil prices higher.
Since the Iran nuclear deal came into effect, Iranian oil output increased from 2.7 million to 3.8 million barrels per day. While the full impact of the USA exit from the nuclear accord is still unclear, the re-imposition of far-reaching sanctions is expected to start reducing shipments from Iran.
European countries said they remained committed to the deal and called on Washington not to prevent other countries from implementing it. That country's rulers are attempting to convince the leaders of Britain, Germany and France, also parties to the 2015 deal, to shun new sanctions.
Setting fire to a paper USA flag and chanting "Death to America", the lawmakers symbolized the anger felt by many Iranians as Trump reneged on the Obama-era deal, signed in 2015 after two years of intense negotiations.
Third, if Iranian crude oil is stymied by U.S. sanctions and the United States banking system is limiting access to finance and insurance, then OPEC will have to open the taps to replace the loss of Iranian crude oil.
Officials are considering whether a drop in Iranian exports and a decline in supply from another OPEC member, Venezuela, demands adjusting the deal that runs to the end of 2018.