Trump warned of "severe consequences" for people or entities that fail to wind down economic activities with Iran.
"We're hopeful that we can find a way to move forward, but it's going to require enormous change on the part of the Iranian regime", Pompeo said.
The rhetoric between the US and Iran remains heated, despite Trump tweeting last week that he would be willing to meet with Iranian President Hassan Rouhani.
Trump has stated he wants a new deal with Iran that goes beyond curbing its nuclear programme, and ends what America calls its "malign influence" in the region, including its support to Syrian President Bashar al-Assad and militant groups in Lebanon and the Palestinian Territories.
The ban on the exchange offices, introduced in March, had left the offices idle overnight: gone were the daily long lines of Iranians waiting to buy or sell dollars. "I don't have pre-conditions". He called on Iranians to unite in the face of hardship.
"We are always in favour of diplomacy and talks. but talks need honesty", he said.
The U.S. has been pushing its allies to halt their import of Iranian oil ahead of the November deadline.
"Preserving the nuclear deal with Iran is a matter of respecting worldwide agreements and a matter of global security", they add. Trump violated the terms of the agreement by reimposing sanctions today, 90 days after he announced the USA would withdraw from it. Administration officials say Iran has used funds freed up by the pact to sow instability across the Mideast. "By returning to the JCPOA", he said, using the technical name for the 2015 nuclear deal. 73 yrs later - w/ vastly expanded nuke arsenal it refuses to dismantle in defiance of NPT commitment - U.S. militarism hasn't faded.
A joint statement issued on Monday by the foreign ministers of the EU's 28 member states, including the UK's foreign secretary, Jeremy Hunt, said there was a "determination to protect" the bloc's economic interests and the nuclear deal known as the joint comprehensive plan of action (JCPOA), which Brussels, along with China and Russian Federation, continues to support.
"We are determined to protect European economic operators engaged in legitimate business with Iran, in accordance with EU law and with United Nations security council resolution 2231".
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"These people came with rocks and broke the sign and all the windows of the prayer house, and they were chanting against the system".
The US official said the European Union move to protect its companies "is not something we're particularly concerned about".
Iran's President Hassan Rouhani said the act was "psychological warfare".
"Trump has already taken a step back from his previous harsh stance", Rouhani said. When Iran's military has lashed out or tested the U.S. in Syria, the United States has beaten them back emphatically, as has Israel.
It is not yet clear how all this will affect ordinary Iranians, but a Western diplomat in Tehran who monitors the economy said prices of basic foods were already creeping up.
Rouhani said "Negotiations with sanctions doesn't make sense".
"Today, the United States is taking action to reimpose nuclear-related sanctions with respect to Iran that were lifted in connection with the Joint Comprehensive Plan of Action of July 14, 2015 (the "JCPOA")".
According to the release, Monday is the final day of a 90-day "wind-down period" since Trump announced the US withdrawal from the deal.
The first wave of sanctions, including a unilateral ban on Iran's access to the U.S. dollar and trade in gold and other precious metals, will kick in on Monday.
"There will be pressure because of sanctions but we will overcome this with unity", he said.