Israel's military said two drones from Yemen had also been intercepted on Monday, two days after the Iran-aligned Houthis entered the war by firing missiles at Israel, and that Lebanon's Hezbollah had fired rockets at Israel.
Israeli forces carried out missile strikes on what they called military infrastructure in Tehran and infrastructure used by Iran-aligned Hezbollah in Beirut, leaving black smoke hanging over the Lebanese capital.
Turkey's defence ministry said a ballistic missile launched from Iran entered Turkish airspace before being shot down by NATO air and missile defences deployed in the eastern Mediterranean.
Iran remained defiant in the month-old war, which began with US-Israeli attacks on Iran on February 28 and has spread across the region, killing thousands, disrupting energy supplies and hitting the global economy.
The majority of those reported killed were in Iran and Lebanon, and many were civilians.
Iran has largely blocked the Strait of Hormuz, a narrow waterway which normally carries about a fifth of global oil and liquefied natural gas supplies.
Iran said on Monday it had received US peace proposals via intermediaries, following talks on Sunday between the foreign ministers of Pakistan, Egypt, Saudi Arabia and Turkey.
But Iranian Foreign Ministry spokesman Esmaeil Baghaei said the proposals were "unrealistic, illogical and excessive".
"Our position is clear. We are under military aggression. Therefore, all our efforts and strength are focused on defending ourselves," he told a press conference.
Soon after Baghaei's remarks, Trump said in a social media post that the United States was in talks with a "more reasonable regime" to end the war in Iran but he also issued a new warning over the Strait of Hormuz.
"Great progress has been made but, if for any reason a deal is not shortly reached, which it probably will be, and if the Hormuz Strait is not immediately 'Open for Business,' we will conclude our lovely 'stay' in Iran by blowing up and completely obliterating all of their Electric Generating Plants, Oil Wells and Kharg Island," Trump wrote.
Trump also threatened a US attack on the desalination plants that supply clean water in Iran.
He said last week he would pause attacks on Iran's energy plants for 10 days, which would be until April 6, US time.
A Pakistani security official, whose country is trying to mediate in the war, said that at this stage it appeared unlikely there would be direct US-Iran talks this week.
"We are trying our best to make it happen as early as possible," the official said.
Baghaei also said Iran's parliament was reviewing a possible exit from the Nuclear Non-Proliferation Treaty, which recognises the right to develop, research, produce and use nuclear energy as long as nuclear weapons are not pursued.
Trump has cited preventing Iran obtaining nuclear weapons as one of the reasons for attacking Iran on February 28.
Iran denies it is seeking a nuclear arsenal.
On Sunday, Trump said the US and Iran had been meeting "directly and indirectly".
But he has also been sending more US troops to the region.
The US Department of Defense is dispatching thousands of troops to the Middle East, giving Trump the option of launching a ground offensive but he has not approved any of those plans, according to multiple news outlets.
Iran has fired on Arab Gulf states during the conflict and war has been reignited between Israel and Hezbollah in Lebanon, where a United Nations peacekeeper from Indonesia was killed when a projectile exploded at one of its positions in southern Lebanon on Sunday.
Another peacekeeper was critically injured.
Iran confirmed on Monday the death of Revolutionary Guards Navy Commander Alireza Tangsiri, the latest of its leaders killed including Supreme Leader Ayatollah Ali Khamenei, who has been replaced by his son Mojtaba Khamenei.
