More than three months after the US and Israel launched strikes against Iran, the conflict is stuck in a stalemate, with a shaky ceasefire in place while the pivotal Strait of Hormuz remains largely shut to maritime traffic.
Iran has not yet responded to a proposed final text of a temporary deal, and was taking a "stern" approach given what it sees as a history of US non-compliance and longstanding mistrust, Mehr News Agency cited a source as saying.
The semi-official Fars agency, also citing a source, added that messages on the possible deal, or memorandum of understanding, had stopped a few days ago, with the last one being Tehran's "clear message" over Lebanon, where Iran is seeking a halt to Israel's incursion against its ally Hezbollah.
Trump said that suggestion was "false and erroneous" and that the conversations between the two sides had continued without a pause.
"The conversations between us have been going on continuously, including four days ago, three days ago, two days ago, one day ago, and today," he said in a social media post.
He made similar comments on Monday, before the Iranian report.
Trump said on Monday there would be a deal over the next week to extend a ceasefire agreed in early April and reopen the strait. Since mid-March, he has repeatedly said he is close to a deal, which would postpone thorny issues including the future of Iran's nuclear program. A ceasefire has largely held since early April, but Iran and the US have exchanged strikes several times over the past week.
US Secretary of State Marco Rubio told Congress on Tuesday that Iran had agreed to negotiate aspects of its nuclear program that it previously refused to discuss, but added that was not a guarantee that negotiations would lead to a deal. Trump has said stopping Iran acquiring nuclear weapons was his top priority. Iran has always denied wanting to build a nuclear bomb, saying its atomic program is for peaceful purposes only.
The war that began on February 28 has killed thousands of people, mainly in Iran and Lebanon. It has caused global pain by pushing up energy prices since Iran effectively closed the Strait of Hormuz, which previously carried about a fifth of global supplies of oil and liquefied natural gas.
Oil prices edged up to a one-week high on Tuesday. It also triggered the latest round of conflict between Israel and Lebanese militant group Hezbollah, with Israel pursuing its deepest incursion into Lebanon in 25 years. On Tuesday, Israel kept up strikes on a string of towns in southern Lebanon, Lebanese security sources said, despite a US-mediated partial ceasefire announced on Monday.
That would entail Israel refraining from strikes on Beirut and Hezbollah-controlled southern suburbs of the Lebanese capital, while the Iran-aligned group would halt attacks on Israel.
But the announcement failed to reassure many Lebanese, 1.2 million of whom have been displaced, and the din of an Israeli drone over Beirut kept residents on edge on Tuesday.
Rubio, who is also Trump's national security adviser, said in testimony to Congress that the US negotiating team had not offered Iran sanctions relief in exchange for reopening the strait, though he said that was the first condition it must meet.
"Iran is being sanctioned because they've highly enriched uranium. Iran is being sanctioned because of their nuclear activities. If they agree to give up those things, there will be sanctions relief associated with their commitment and compliance with those agreements," he said.
