The New York Times | �Farnaz Fassihi�and�Rick Gladstone: President Hassan Rouhani of Iran said Friday that President Trump had offered to meet with him at the United Nations this week and then lift all sanctions, but that Mr. Rouhani declined because the �optics� of such a meeting were unacceptable.

Mr. Rouhani�s assertions, reported on his website as he returned home from the United Nations General Assembly, were quickly disputed by Mr. Trump on Twitter.

�Iran wanted me to lift the sanctions imposed on them in order to meet,� Mr. Trump said. �I said, of course, NO!�

The contradictory narratives added a new twist to the frantic diplomacy that America�s allies at the United Nations engaged in while trying to arrange a meeting between Mr. Trump and Mr. Rouhani, in an effort to halt spiraling tensions between the United States and Iran.

Mr. Trump has imposed onerous economic sanctions on Iran since he abandoned the 2015 nuclear agreement last year, calling it �a disaster� that would not deter Iran from making nuclear weapons.

Iran has responded by halting its compliance with some provisions of the agreement while insisting that it would return to compliance � if the sanctions were lifted first and if the United States rejoined the agreement.

Tensions have been further roiled by American and Saudi Arabian accusations that Iran attacked oil facilities in Saudi Arabia on Sept. 14 � accusations that Britain, France and Germany have now joined. The Iranians have denied responsibility for the attack and have warned that retaliation would invite war.

Mr. Rouhani told a news conference in New York on Thursday as he was about to leave for home that if the Trump administration first dropped all the sanctions, �then negotiations with the U.S. are a possibility.�

On Friday, Mr. Rouhani said more about what he described as the diplomatic efforts to arrange a meeting with Mr. Trump and Iran�s response.

�The Americans had sent a message through nearly all European leaders that they are ready to negotiate,� Mr. Rouhani said, according to his website. �The U.S.�s request was for bilateral talks, meaning the two presidents negotiate with each other, and we had rejected this many times.�

He said Iran was willing to negotiate with the United States as part of a meeting with the other members of the 2015 nuclear agreement � Britain, China, France, Germany and Russia.

�The German chancellor and the U.K. prime minister and France�s president were all in New York and they were all insisting that this meeting happen and the U.S. saying it would lift all sanctions,� Mr. Rouhani said.

He said they had discussed which sanctions would be lifted and in what order, and that �the U.S. government said very clearly that it would lift all sanctions.�

But Mr. Rouhani said that �the optics of this were not the kind of optics that would be acceptable to us.�

Such a meeting, he said, would mean that Iran would have been negotiating with the United States �in the atmosphere of maximum pressure and sanctions,� which Mr. Rouhani has repeatedly said he would not do.

The spokesman for Iran�s United Nations Mission, Alireza Miryousefi, elaborated on Mr. Rouhani�s response in his own Twitter account, saying that the Iranian president had insisted that the United States would �first have to create the proper environment by removing the poisonous atmosphere of sanctions.�

Political analysts who follow Iran said the posturing on both sides that followed the failed diplomacy suggested that Iran was still interested in talking.

�The major hangup was choreography and sequencing,� said Ali Vaez, the Iran director for the International Crisis Group. �But the idea is not dead, and the main quid pro quo remains viable.�

Mr. Rouhani�s portrayal of his dealings at the United Nations also seemed partly aimed at countering the appearance of Iran�s isolation this year at the international gathering, particularly over the attack on the Saudi oil facilities.

He challenged the leaders of Britain, France and Germany for evidence that Iran had been responsible for the attack.

�They did not have any answer,� Mr. Rouhani said. �I said I�ll be waiting in Tehran to receive your evidence.�

Even as the Europeans were seeking to arrange a meeting between Mr. Trump and Mr. Rouhani, the Trump administration was intensifying sanctions on Iran. On Wednesday, the State Department barred top Iranian officials from entering the United States and confined those visiting the United Nations to a tight radius of a few city blocks.

The visa restriction had an immediate impact on Foreign Minister Mohammad Javad Zarif of Iran, who wanted to visit the country�s United Nations ambassador, Majid Takht-Ravanchi, a patient at the Sloan Kettering Memorial Cancer Center a mile away. The State Department rejected the request.

�Foreign Minister Zarif would like to visit a colleague who is in the hospital receiving world-class care,� the State Department said in a statement confirming the rejection of his request, which was first reported by Foreign Policy magazine.

�Iran has wrongfully detained several U.S. citizens for years, to the pain of their families and friends they cannot freely visit,� the statement said. �We have relayed to the Iranian mission that the travel request will be granted if Iran releases a U.S. citizen.�

In a positive development on Friday against otherwise tense relations with the West, a British-flagged oil tanker seized by Iran two months ago near the Persian Gulf was finally permitted to leave Iran�s southern port of Bandar Abbas, and it headed for Dubai. Iran had impounded the ship, the Stena Impero, in apparent retaliation for the British seizure of an Iranian tanker near Gibraltar that was later released.

Lara Jakes contributed reporting from Washington, and Michael Wolgelenter from London.