US President Donald Trump has insisted he did not offer to lift sanctions on Iran.
Iranian President Hassan Rouhani claimed on Friday that the US offered to remove all sanctions in return for talks.
Mr Rouhani added that Tehran had not accepted the offer due to the "toxic atmosphere".
But Mr Trump responded in a tweet: "Iran wanted me to lift the sanctions imposed on them in order to meet. I said, of course, NO!!
Mr Rouhani, speaking on his return from the United Nations General Assembly in New York, said he met there with US officials at the insistence of the UK, Germany and France.
"It was up for debate what sanctions will be lifted and they (the US) had said clearly that we will lift all sanctions," Mr Rouhani said, according to his official website.
Iran was ready for negotiations but not in an atmosphere of sanctions and pressure, the Iranian president said.
"This action wasn't in a manner that was acceptable, meaning that in the atmosphere of sanctions and the existence of sanctions and the toxic atmosphere of maximum pressure, even if we want to negotiate with the Americans in the 5+1 framework, no one can predict what the end and result of this negotiation will be," he said.
Mr Rouhani did not meet Mr Trump in New York and European and Gulf officials expect Washington to keep tightening the vice on Iran's economy.
The US and Iran are at odds over a host of issues, including the US withdrawal from the 2015 Iran nuclear deal and US accusations - denied by Tehran - that Iran attacked two Saudi oil facilities.
There is also tension over Iran's detention of US citizens on what the United States regards as spurious grounds.
After denying claims the US offered to lift sanctions, Mr Trump then addressed another ongoing issue as he tweeted: “IT WAS A PERFECT CONVERSATION WITH UKRAINE PRESIDENT!”
He added: "Rep. Adam Schiff totally made up my conversation with Ukraine President and read it to Congress and Millions.
"He must resign and be investigated. He has been doing this for two years. He is a sick man!
"The Democrats are now to be known as the DO NOTHING PARTY!"
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