Foreign Minister Mohammad Javad Zarif ruled out talks with Secretary of State Mike Pompeo.
Mr Trump slapped tough sanctions on Iran earlier this month despite pleas from the international community.
The US President claimed they were “the most biting sanctions ever imposed” with Iran shooting down suggestions of negotiations at the United Nations General Assembly.
Mr Zarif told Iranian news agency Tasnim: «No such meeting is planned. We have repeatedly announced our position.
«About the recent offer by Trump, our official position has been announced both by the president (Rouhani) and myself.
“The Americans lack honesty.”
Trump has threatened to blacklist trading partners and companies doing business with Iran.
China and EU members have slammed the US leader’s move.
No meeting is planned. The Americans lack honesty.
Iran Foreign Minister Mohammad Javad Zarif
Mr Trump claims he wants to convince Iran to agree to a new nuclear accord after he pulled the US out of a 2015 agreement.
Trump tweeted: “The Iran sanctions have officially been cast.
“These are the most biting sanctions ever imposed, and in November they ratchet up to yet another level.
“Anyone doing business with Iran will NOT be doing business with the United States.
“I am asking for WORLD PEACE, nothing less!”
Mr Zarif also denied a message from Washington would be delivered to Iran by Omani officials.
Oman and Switzerland had acted as mediators in talks with America in the past.
Meanwhile, Iran has leapt to Turkey’s defence as Trump slapped tariffs on its NATO partner.
Mr Zarif accused the US of «bullying» and appeared to threaten Washington.
He said: «The U.S. has to rehabilitate its addiction to sanctions & bullying or entire world will unite — beyond verbal condemnations — to force it to.»