The missiles triggered air raid sirens in parts of Israel, including Tel Aviv where blasts from interceptions were heard.
In one attack, homes in northern Israel were damaged by falling debris following an interception. No deaths were reported.
Trump wrote on his Truth Social platform on Monday that the US and Iran had held "very good and productive" conversations about a "complete and total resolution of hostilities in the Middle East".
As a result, he said, he was postponing for five days a plan to hit Iran's energy grid.
His announcement on Monday sent share prices higher and oil prices sharply lower to below $US100 a barrel, a sudden reversal to a market swoon caused by his weekend threats and Iran's vows to respond.
Those gains were in jeopardy on Tuesday, however, after Iran's powerful parliament speaker Mohammad Baqer Qalibaf - who an Israeli official and two other sources familiar with the matter said was the interlocutor in the talks on the Iranian side - said no negotiations had taken place.
"No negotiations have been held with the US, and fake news is used to manipulate the financial and oil markets and escape the quagmire in which the US and Israel are trapped," he wrote on X.
Iran's elite Revolutionary Guards said they were launching fresh attacks on US targets, and described Trump's words as "psychological operations" that were "worn out" and having no impact on Tehran's fight.
Global markets rallied in relief overnight after Trump added five days to his Saturday ultimatum for Iran to reopen the Strait of Hormuz - a conduit for about 20 per cent of the world's oil and liquefied natural gas - within 48 hours.
But on Tuesday those gains were under threat as markets weighed the conflicting messages from Tehran and Washington.
Trump told reporters his special envoy Steve Witkoff and son-in-law Jared Kushner, who had been negotiating with Iran before the war, had held discussions with a top Iranian official.
"We have had very, very strong talks. We'll see where they lead. We have major points of agreement, I would say, almost all points of agreement," he said on Monday.
A European official said that while there had been no direct negotiations between the two nations, Egypt, Pakistan and Gulf states were relaying messages.
A Pakistani official and a second source told Reuters that direct talks on ending the war could be held in Islamabad as soon as this week.
Israeli Prime Minister Benjamin Netanyahu said in a video statement that he spoke with Trump on Monday and that Israel would press on with attacks in Lebanon and Iran.
Although there was no immediate confirmation that talks had taken place as described by Trump, Iran's foreign ministry described initiatives to reduce tensions.
It said Iranian Foreign Minister Abbas Araqchi had reviewed developments related to the Strait of Hormuz with his Omani counterpart and agreed to continue consultations between the two countries.
The Pakistani official said US Vice-President JD Vance, as well as Witkoff and Kushner, were expected to meet Iranian officials in Islamabad this week, following a call between Trump and Pakistan's army chief Asim Munir.
Iran has effectively closed the key Strait of Hormuz since the United States and Israel launched their war on the country on February 28.
More than 2000 people have been killed in the war.
Iran had responded to Trump's threats to strike its power plants by saying it would hammer the infrastructure of US allies in the Middle East, raising the prospect that an extreme disruption to global energy supplies could last longer than previously expected.
