Rouhani, speaking on his return from the United Nations General Assembly in New York said Germany, Britain and France had insisted on a joint meeting with U.S. officials.
"The German chancellor, the prime minister of Britain and the president of France were in New York and all insisted that this meeting take place and America says that it will lift the sanctions," Rouhani said, according to his official website.
"It was up for debate what sanctions will be lifted and they (the United States) had said clearly that we will lift all sanctions," his website quoted him as saying.
U.S. President Donald Trump tweeted on Friday that he had rejected Iran's request to lift sanctions.
"Iran wanted me to lift the sanctions imposed on them in order to meet. I said, of course, NO!" he wrote.
Iran wanted me to lift the sanctions imposed on them in order to meet. I said, of course, NO!— Donald J. Trump (@realDonaldTrump) September 27, 2019
According to Rouhani, France and Britain pressed him to meet Trump, with French President Emmanuel Macron warning him it would be a lost opportunity if he did not. British Prime Minister Boris Johnson suggested the Iranian leader should take the plunge.
Iran has ruled out bilateral talks with the United States unless it returns to the 2015 Iran nuclear deal, abandoned by Trump last year, and eases the crippling economic sanctions that he has since imposed on the Islamic Republic.
Iran was ready for negotiations but not in an atmosphere of sanctions and pressure, Rouhani said.
Rouhani did not meet Trump in New York and European and Gulf officials expect Washington to keep tightening the vice on Iran's economy.
The United States and Iran are at odds over a host of issues, including the U.S. withdrawal from the 2015 Iran nuclear deal, U.S. accusations - denied by Tehran - that Iran attacked two Saudi oil facilities on Sept. 14, and Iran's detention of U.S. citizens on what the United States regards as spurious grounds.