But in a softer approach, Trump told reporters on Thursday at the White House: "What I would like to see with Iran, I would like to see them call me".
Iranian President Hassan Rouhani has slammed the "unprecedented" United States pressure on Tehran and urged unity among the country's political factions to overcome conditions which he said may be harder than those during the 1980s.
Separately, he said the worldwide community admits the White House's "wrong policies" and its "mistake" to pull out of the Iran nuclear deal and intensify pressure on Iran.
MARAD said US-flagged ships were encouraged to contact the Fifth Fleet at least two days before sailing through the Strait of Hormuz.
Iranian navy commander Rear Admiral Hossein Khanzadi said on Sunday that American forces must exit the Gulf, according to ISNA.
The U.S. military has sent forces, including an aircraft carrier and B-52 bombers, to the Middle East to counter what U.S. officials have said are "clear indications" of threats from Iran to its forces there.
He added: 'The American sanctions are breaking the neck of the Iranian economy, and a new and stronger wave [of sanctions] is still to come'.
"Negotiations with Americans will not take place, and Americans will not dare to take military action against us", said IRGC Lieutenant Commander for Political Affairs Brigadier General Yadollah Javani.
"Most of all we need to make sure that we don't end up putting Iran back on the path to re-nuclearization", he said.
The administration continues to suggest that its goals are a new, more comprehensive agreement with Iran-on Thursday, Trump said that if Iran reached out to him "we can make a fair deal"-but its actions have made that goal more elusive".
Trump announced that he is open to talks with the Iranian leadership.
The UK, Germany and France have established the Instrument for Trade and Exchanges (INSTEX) in a bid to satisfy Iran's demands for trade despite usa sanctions. On Friday, Iran rejected the offer of talks from Trump.
Iranian officials rebuffed President Donald Trump's suggestion that they call him to try to defuse frictions as the US ratcheted up its actions against Tehran.
"Our restraint to this point should not be mistaken by Iran for a lack of resolve", he said, adding however: "We do not seek war".
Iranian officials have also dismissed the allegations as part of the United States administration's "psychological warfare" against the country.
They said that there can be no preconditions before any potential talks.
In the three-decade old military confrontation with the warring neighbour, none from the worldwide community had slapped Iran with sanctions on import, export and oil sales.
In May previous year, Trump pulled the United States out of an agreement aimed at curtailing Iran's nuclear ambitions and reinstated unilateral economic sanctions.
And acting U.S. defence secretary Patrick Shanahan said called on Iran to "cease all provocation" and said they would hold the regime accountable for "any attack on USA forces or interests".