"It is a commercial decision for companies whether they continue to work in Iran", Burt said.
"These are the most biting sanctions ever imposed, and in November they ratchet up to yet another level".
The EU has taken the unprecedented step in a bid to salvage the nuclear deal struck with Iran in 2015.
Trump said he was open to reaching a more comprehensive deal with Iran "that addresses the full range of the regime´s malign activities, including its ballistic missile program and its support for terrorism".
Looming US sanctions against Iran will likely hit Tehran's oil sales overseas, and it could lead to a price spike in oil contracts. She made the announcement on the same day renewed US trade sanctions against the Islamic Republic restarted.
"We are always in favor of diplomacy and talks".
Responding to Mr. Trump's comments, Iran's President Hassan Rouhani said that Washington's call for new nuclear negotiations at the same time the USA reimposes crippling sanctions "makes no sense".
President Trump withdrew the U.S. from the Iran nuclear deal earlier this year, and began reimposing sanctions on Iran Monday.
"I want to make this very clear because we're talking about trade and economic relations with Iran because - this is an integral part of the nuclear deal".
The "Trump Administration wants the world to believe it's concerned about the Iranian people", Iranian foreign minister Mohammad Javad Zarif said in a statement posted to Twitter.
The second phase of United States sanctions, which takes effect November 5 and will block Iran's oil sales, is due to cause more damage, though several countries including China, India and Turkey have indicated they are not willing to entirely cut their Iranian energy purchases.
The European Union, which remains a supporter of the three-year-old nuclear pact with Iran, said it is taking counter-measures to blunt the impact of the sanctions Trump has reinstituted. "Anyone doing business with Iran will NOT be doing business with the United States", he wrote.
His warning was apparently meant at the European Union which put into force a law banning companies from complying with United States sanctions or court rulings and enabling them to claim compensation for potential damage. "But talks need honesty".
But on Iran, Mr Trump now has a team who share his contempt for the regime and are even more determined to see its end.
There have been protests in Iran against rising prices, and the government has responded firmly.
Iran's foreign minister Mohammad Javad Zarif told reporters the global reaction to Trump's move showed that the USA was diplomatically "isolated", but acknowledged the sanctions "may cause some disruption".
But the last two days have seen an impressive 20 percent rally in the value of the rial after the government announced new foreign exchange rules and launched a corruption crackdown that included the arrest of the central bank's currency chief.
There have been ongoing rumours that Trump and Rouhani could meet in NY in September at the United Nations General Assembly - though Rouhani reportedly rejected USA overtures for a meeting at last year's event.