"The Fake News put out a typically false statement, without any knowledge that the United States was trying to set up a negotiation with Iran. This is a false report," Trump wrote in a tweet that did not specify what report he was referring to.
....Iran will call us if and when they are ever ready. In the meantime, their economy continues to collapse - very sad for the Iranian people!
On Sunday, Trump had said that if Iran wanted to fight then it would be "official end of Iran". Never threaten the United States again," Trump had said in a tweet as tensions between the two countries continued to simmer.
The US had sent B-52 bombers and warships to the Gulf as tensions between the two countries reached fever pitch last week. The Trump administration has ordered non-essential diplomatic staff out of Iraq over Iran row.
Meanwhile, Iran's foreign minister Mohammad Javad Zarif said that the "genocidal taunts" of US President Donald Trump will not "end Iran". "Iranians have stood tall for millennia while aggressors all gone. Economic terrorism and genocidal taunts won't 'end Iran'," Zarif wrote on Twitter.
Relations between the two countries had hit rock bottom last year when Trump pulled out of the 2015 nuclear deal with Iran and imposed tough sanctions, a move criticised by the European Union which backed Iran.
The United Nations voiced concern about the rising rhetoric between the United States and Iran and called on the two sides to dial down their remarks.
"We would ask all parties to lower the rhetoric and lower the threshold of action as well," said UN spokesman Stephane Dujarric, adding,"we are concerned about the rising rhetoric."
As tensions mounted, on Sunday a rocket was fired into the Green Zone of the Iraqi capital Baghdad, which houses government offices and embassies including the US mission. It was not immediately clear who was behind the attack.
On Sunday, Trump had said that if Iran wanted to fight then it would be "official end of Iran".