The conflicting statements came as the economic and humanitarian toll of the war mounted, with fuel shortages spreading worldwide, sending companies and countries scrambling to contain the fallout.
Iranian Foreign Minister Abbas Araqchi said while there had been no dialogue or negotiation with the US, various messages had been exchanged through intermediaries.
"Messages being conveyed through our friendly countries and us responding by stating our positions or issuing the necessary warnings is not called negotiation or dialogue," Araqchi said in a state television interview on Wednesday.
Trump, speaking later on Wednesday at an event in Washington, said Iranian leaders "are negotiating, by the way, and they want to make a deal so badly, but they're afraid to say it because they will be killed by their own people. They're also afraid they'll be killed by us."
Even if they happen, any negotiations would likely prove very difficult, given the maximalist positions laid out by both sides.
A 15-point US proposal to end the conflict, sent to Iran via Pakistan, includes demands ranging from dismantling Iran's nuclear program and curbing its missiles to effectively handing over control of the Strait of Hormuz, according to sources and reports.
But 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.
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.
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.
Israel's military said it had completed a wide-scale wave of strikes targeting infrastructure in Iran.
Iranian supreme leader Ayatollah Ali Khamenei was killed on the first day of the conflict by an Israeli strike and was replaced by his son Mojtaba, who has been wounded in strikes and not been seen since his appointment.
Israel took Iran's foreign minister Araqchi and parliamentary speaker Mohammad Baqer Qalibaf off its hit-list after Pakistan asked Washington not to target them, a Pakistani source told Reuters on Thursday.
An Iranian embassy official in Islamabad said talks in Islamabad were still on the table and Pakistan was the preferred venue for Tehran, although nothing had been finalised.
A senior Israeli defence official said Israel was sceptical Iran would agree to terms proposed by the US, and that Israel was concerned US negotiators might make concessions.
The fallout from the conflict, which has caused the worst energy shock in history, has spread far beyond the region.
With the Strait of Hormuz, a conduit for a fifth of the world's oil and liquefied natural gas, effectively closed, businesses from airlines to supermarkets are grappling with challenges including rising costs, weakening demand and disrupted supply chains.
A Reuters/Ipsos poll conducted March 20-23 found 61 per cent of Americans disapproving of US military strikes in Iran, while 35 per cent approved.
Exchanges of missiles and drones across the Gulf continued on Thursday. In Abu Dhabi, two people were killed and three others injured by debris from an intercepted ballistic missile, the government said.
Admiral Brad Cooper, head of US forces in the Middle East, told reporters that Iran's drone and missile launch rates were down more than 90 per cent.
