"I'd say we're in a period where the threat remains high and our job is to make sure that there is no miscalculation by the Iranians", he said. "If they do something, it will be met with great force but we have no indication that they will".
But Zarif said that Iran is "not going to talk to people who have broken their promises".
Two influential Shiite figures in Iraq are warning from pulling their country into a war between the United States and Iran, saying it would turn Iraq into a battlefield and inflict much harm. Saudi Arabia accused Tehran of ordering the attack.
Tensions between Washington and its Sunni Muslim Gulf Arab allies on one side and Tehran and its Shi'ite Muslim proxies in the region on the other have been flaring for weeks.
On Wednesday, the US cited growing yet unspecified threats as it ordered the departure of non-emergency staff from Iraq, where Iran provides material and political support to several powerful militias.
"Pompeo made the comments in a Fox News Radio interview with Guy Benson on Thursday amid the increasing tensions between the USA and Iran, and the calls to investigate Kerry, the former secretary of state under President Obama, over the alleged violations of the Logan Act for meeting with Iranian officials", reports Fox News.
At the outset of an investigation into those apparent attacks, which damaged vessels of Saudi Arabia, the UAE and Norway but caused no injuries, USA officials had said they appeared to be carried out by Iran.
Relations between Washington and Tehran plummeted a year ago when Trump pulled out of a landmark 2015 nuclear deal with Iran and imposed tough sanctions.
Supreme Leader Ayatollah Ali Khamenei said Tehran would not negotiate another deal and Tehran has notified the five remaining signatories, which include the United Kingdom, that it would reduce some commitments under the treaty.
On Monday, semi-official news agencies in Iran reported that the country has quadrupled its production of low-enriched uranium.More news: Real Madrid boss Zidane: Barcelona UCL exit doesn't change our season
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But Mr Trump's tweet marked a shift in tone after recent attempts by him to downplay the possibility of a military conflict with Iran.
Tehran has dismissed the USA allegations, and accused Washington of an "unacceptable" escalation of tensions.
Under the deal, Iran can only enrich uranium at 3.67% - suitable for a power plant and far below the 90% required for weapons grade. One missile was stopped over the city of Taif and the other over Jiddah. He said Iran took this step because the USA had ended a program allowing it to exchange enriched uranium to Russian Federation for unprocessed yellowcake uranium, as well as ending the sale of heavy water to Oman.
While the U.S. claim of Iranian "threats" has been met with widespread scepticism outside the United States, the mounting tensions have sparked growing worldwide concern.
"The enemy constantly wanted Iran to start the tension, but we did not do it", he said. "Recalling "other aggressors" such as Genghis Khan and Alexander the Great, Zarif tweeted that "Iranians had stood tall for millennia" and that "#EconomicTerrorism and genocidal taunts won't end Iran".
Leading Iraqi Shia figures with close ties to Iran warned on Monday against attempts to pull their country into a war between the United States and Tehran.
Since then, the Trump administration has pursued a "maximum pressure" campaign against Tehran, which it accuses of being a destabilising actor in the Middle East.
Iran's U.N. Ambassador Majid Takht Ravanchi warned U.N. Secretary-General Antonio Guterres in a letter made public on Monday that "if unchecked, the current situation might - sooner or later - go beyond the perimeter of control and thereby lead to another unnecessary regional crisis".