Israel hit a petrochemical plant in southwestern Iran that it said was used to produce ballistic missiles, and Iran's Islamic Revolutionary Guard Corps (IRGC) said it retaliated with a strike aimed at a similar Israeli facility in the city of Haifa.
The exchange followed Israeli strikes on strongholds of Iran-backed Hezbollah in Beirut at the weekend.
Tehran has repeatedly said any deal with Washington to end the conflict must include a halt to Israel's campaign in Lebanon.
"Israel and Iran must immediately stop 'shooting'," Trump said posted on Truth Social, a day after he told Israeli Prime Minister Benjamin Netanyahu to refrain from further attacks to avoid undermining the peace talks with Tehran to end the more than three-month-old conflict.
An Israeli military official said on Monday his country was prepared for a range of options in Iran, from several days to "as long as it takes", adding that it had struck Iranian air defence systems that were being rebuilt after previous Israeli attacks, as well as the petrochemical plant.
In a similarly defiant vein, an Iranian military source quoted by the Tasnim news agency said Tehran was prepared for a prolonged conflict with Israel and for renewed strikes against US interests in the region.
Iranian media later reported the sound of explosions in Tehran on Monday, and the semi-official Mehr news agency said air defences had shot down a drone over the capital.
Yemen's Iran-aligned Houthis pledged to stop Israel's maritime navigation in the Red Sea, and said it was behind the first missile attack on Israel since an April 8 ceasefire that paused all-out warfare.
The Israeli military official said Iran had fired "close to 30 ballistic missiles" at Israel since Sunday evening, and the Houthis a further two missiles.
Israel activated its aerial defence systems to repel most of the incoming strikes.
Israel said it struck targets at the Mahshahr petrochemical complex that were used to produce and export raw materials for Iran's missile program.
The IRGC said it had targeted Ramat David air base, near Nazareth, on Sunday.
Israel said it identified missiles launched from Iran and its defence systems had intercepted them.
Trump has leaned on Israel to stop its attacks on Iran-backed Hezbollah in Lebanon to allow room for a deal to end the wider war with Iran.
However, Israel launched strikes on Hezbollah strongholds in the Beirut area on Sunday for the first time since the US announced a truce plan for Lebanon on June 3.
Iran fired salvos of missiles at Israeli targets in retaliation, but Trump insisted that an agreement to end the wider war remained within reach.
Trump told Netanyahu during Sunday's call to refrain from further strikes because "we are close to doing something good in terms of a deal", according to a US official quoted by Axios.
Israel has never halted its Lebanon campaign, which has killed thousands of people and driven hundreds of thousands more from their homes, saying it should be treated separately from any Iran ceasefire.
Hezbollah, which kept out of truce talks, has also continued its attacks and says it will not give up its weapons unless Israel halts its attacks and withdraws from Lebanon.
Tehran has long said any peace deal with the US would depend on a ceasefire also holding in Lebanon, which Israel invaded in March in pursuit of Hezbollah fighters who fired across the border in solidarity with Tehran.
The US ambassador to Lebanon, Michel Issa, said on Monday that Lebanese-Israeli negotiations were scheduled to resume in Washington.
Despite the April ceasefire, there have been sporadic flare-ups of fighting in the Gulf.
Tehran has blocked most shipping through the Strait of Hormuz, which carried a fifth of the world's crude oil and liquefied natural gas before the war.
Washington has imposed its own blockade of Iranian ports.
