The Iranian official said the proposal, conveyed via Pakistan, "was reviewed in detail on Wednesday night by senior Iranian officials and the representative of Iran's Supreme Leader".
It lacked the minimum requirements for success and served only US and Israeli interests, the official said, while stressing that diplomacy had not ended despite the lack for now of a realistic plan for peace talks.
Trump described the Iranians as "great negotiators" but added that he was not sure he was "willing to make a deal with them to end the war".
Iran has launched strikes against Israel, US bases and Gulf states as well as effectively blocking Middle East fuel exports via the Strait of Hormuz since the US and Israel attacked Iran on February 28.
"They now have the chance, that is Iran, to permanently abandon their nuclear ambitions and to join a new path forward," Trump said during a cabinet meeting at the White House.
"We'll see if they want to do it. If they don't, we're their worst nightmare. In the meantime, we'll just keep blowing them away."
Oil jumped to $US105 a barrel on Thursday and stock markets fell on renewed pessimism over ceasefire prospects as global plastics, technology, retail and tourism struggled with the effects.
Trump suggested on Thursday that Iran let 10 oil tankers transit the Strait of Hormuz as a goodwill gesture in negotiations, including some Pakistan-flagged vessels, elaborating on what he had described as a "present" from Iran.
The president, who is expected to send thousands of troops to the Middle East, driving expectations of a ground invasion, also said taking control of Iran's oil was an option but gave no further details.
US Special Envoy Steve Witkoff confirmed that the United States had sent a "15-point action list" as a basis for negotiations to end the war.
Pakistan's foreign minister said "indirect talks" between the US and Iran were taking place through messages relayed by his country, with other states including Turkey and Egypt also supporting mediation efforts.
Any talks, were they to happen, would likely prove very difficult given the positions laid out by both sides.
According to sources and reports, the 15-point proposal includes demands ranging from dismantling Iran's nuclear program and curbing its missiles to effectively handing over control of the strait.
Iran has hardened its stance since the war began, demanding guarantees against future military action, compensation for losses, and formal control of the strait, Iranian sources say.
It also told intermediaries that Lebanon must be included in any ceasefire deal, regional sources said.
Earlier on Thursday, Trump has warned Iran to "get serious" about a deal to end the fighting.
Trump said in a post on Truth Social that Iran had been "militarily obliterated, with zero chance of a comeback" and was "begging" for a deal.
Calling Iranian negotiators "very different and 'strange'," he added: "They better get serious soon, before it is too late, because once that happens, there is NO TURNING BACK, and it won't be pretty."
Trump has not identified who the US is negotiating with in Iran, with many high-ranking officials among the thousands of people killed across the Middle East since the US and Israel attacked Iran on February 28.
Iran has since launched strikes against Israel, US bases and Gulf states.
An Iranian embassy official in Islamabad said talks in the city were still on the table and Pakistan was the preferred venue for Iran.
On Thursday, Iran launched multiple waves of missiles at Israel, triggering air raid sirens in Tel Aviv and other areas and injuring at least five people.
In Iran, strikes hit a residential zone in the southern city of Bandar Abbas and a village on the outskirts of the southern city of Shiraz, where two teenage brothers were killed, Iran's Tasnim news agency said.
A university building in Isfahan was reported to have been hit.
Israeli officials said Israel had killed the naval commander of Iran's Revolutionary Guards, and that it had many more targets left as it degraded Iranian capabilities.
Still, Israel took Araqchi and Iranian parliament Speaker Mohammad Baqer Qalibaf off its hit-list after Pakistan urged the US to press Israel not to target people who could be negotiating partners, a Pakistani source with knowledge of the discussion told Reuters.
