Secretary of State Mike Pompeo said in a statement that "this action was taken as part of the administration's maximum pressure campaign against the Iranian regime which has engaged in 40 years of terror and aggression against the United States and our allies".
"Media asked if the claimed cyberattacks against Iran are true", he said, adding, "We have been under cyber-terrorism attacks like Stuxnet and unilateralism - like the United States sanctions - for a long time", but none have been successful.
On Monday, Pompeo held separate talks with King Salman and Crown Prince Mohammed bin Salman in the Saudi port city of Jiddah to discuss the escalation with Iran.
From the kingdom, Pompeo will travel to neighbouring United Arab Emirates, another close U.S. ally.
Tehran has denied involvement in the tanker attacks, which no one has claimed responsibility for.
In what it says are defensive moves, the USA has built up its military presence around the Persian Gulf in recent weeks.
The semi-official Tasnim news agency carried Rear Admiral Hossein Khanzadi's warning made during a meeting with a group of defence officials. "I know many Iranians living in NY, and they're fantastic people", Trump said in response to a question.
A multinational accord reached by Tehran and world powers in 2015 sought to curb Iran's nuclear ambitions in exchange for sanctions relief.
The targets of the new sanctions include senior military figures in Iran, blocking their access to any financial assets under US jurisdiction.
Tensions between the U.S. and Iran have increased dramatically in recent weeks after a number of oil tankers were attacked and sabotaged in multiple incidences in the Arab-Persian Gulf, which the United States and its allies in the region have accused Iran of conducting.
Iran dismissed the cyber attacks as a failure. Drones were also used to attack a Saudi oil pipeline last month.
Saudi Arabia has been at war with the Houthis for more than four years.
"We were cocked & loaded to retaliate last night on 3 different sights when I asked, how many will die", Trump tweeted.
"The US offer for negotiations with no precondition is not acceptable while sanctions and threats continue".
"We have been doing everything we can to de-escalate the situation", Mr Hunt said.
Tehran has always been in a "campaign of aggression" against its Arab neighbours, the U.S. and Israel, Netanyahu said, and recent tensions were not a result of increasing USA pressures.
Iran shot down the drone, saying it was in its air space, which Washington disputes. The President's order will deny Iran's leadership access to financial resources and authorises the targeting of persons appointed to certain official or other positions by the Supreme Leader or the Supreme Leader's Office. Citing those episodes and intelligence about other Iranian threats, the USA has sent an aircraft carrier to the Persian Gulf region and deployed additional troops alongside the tens of thousands already there.
Mnuchin told reporters Zarif would be added to an economic sanctions list "later this week", adding that eight top military commanders from Iran's Revolutionary Guards have now also been blacklisted.