As sirens rang out in Jerusalem, Israel's army said it had responded to fresh Iranian missiles, while local Iranian media reported new explosions in Tehran that caused "power outages in parts" of the capital.
Iran, meanwhile, fired a new salvo of missiles at Gulf nations.
In Dubai, four people were wounded by falling debris from intercepted projectiles while an Iranian attack sparked a fire at a Kuwaiti oil tanker in the city's port, said authorities in the financial hub whose reputation for stability has been shaken by the conflict.
In Saudi Arabia, authorities said they intercepted eight ballistic missiles, hours after Iran's top diplomat called on Riyadh to "eject US forces".
Trump threatened Monday that if Iran did not strike a deal -- which included reopening the vital Strait of Hormuz shipping lane -- US forces would destroy "all of their Electric Generating Plants, Oil Wells and Kharg Island (and possibly all desalinisation plants!)."
But the Wall Street Journal reported he also told aides he was willing to end the war even if the strait remains largely closed — likely strengthening Tehran's control over the waterway.
Refusing to back down, an Iranian parliamentary committee voted to impose tolls on vessels in the strait, the passageway through which one-fifth of global oil passes, and completely ban ships from the United States and Israel.
The Strait had been open before the war, and still is for non hostile vessels, but US Secretary of State Marco Rubio has recently spoken of building a "coalition" to oppose a potential Iranian tolling plan.
"So this means that nations can now take over international waterways and claim them as their own," Rubio told Al-Jazeera of the waterway the US president recently called the "Strait of Trump".
For Israel's part, Prime Minister Benjamin Netanyahu claimed his army had achieved key objectives, including "wiping out" industrial plants in Iran and coming "close to finishing their arms industry".
"It's definitely beyond the halfway point. But I don't want to put a schedule on it," Netanyahu told US broadcaster Newsmax.
Israel's army also reported Tuesday that four more of its soldiers had been killed in combat in southern Lebanon, where the war has spilt and where they are clashing with resistance group Hezbollah.
Stop the war
Trump said the United States claimed speaking to a "more reasonable regime" in Tehran, which has denied any talks and accused him of lying about negotiations as cover while readying a ground invasion.
But Iranian foreign ministry spokesman Esmaeil Baqaei again denied any negotiations, saying the United States had sent only a request to talk via intermediaries, including Pakistan.
The war, and the spiralling price of oil, have been unpopular in the United States, where Rubio again said Monday that it would last "weeks" more and not months.
Egyptian President Abdel Fattah al-Sisi, whose country is feeling the economic pinch of the war, appealed directly to Trump to find an offramp.
"Please, help us to stop the war; you are capable of it," Sisi said.
Pakistani Foreign Minister Ishaq Dar, whose country is acting as an intermediary between Tehran and Washington, was set to travel to Beijing for talks on Tuesday on "global issues of mutual interest" with counterpart Wang Yi.
Dar hosted foreign ministers from Saudi Arabia, Egypt and Turkey in the Pakistani capital on Sunday, saying Islamabad was ready to host talks between the United States and Iran in the "coming days".
After weeks of strikes, residents of Tehran painted a picture of a city that is still clinging to some routine despite tight security.
"When I make it to a cafe table, even for a few minutes, I can almost believe the world hasn't ended," said Fatemeh, 27, a dental assistant.
"And then I go back home, back to the reality of living through war, with all its darkness and weight."
Lebanon pounded
On another front, Israel has relentlessly pounded Lebanon, including central Beirut, an hit the UN peacekeepers mission in the South.
The UNIFIL said that two Indonesian peacekeepers were killed when "an explosion of unknown origin destroyed their vehicle", with two other peacekeepers wounded, one seriously. Another Indonesian peacekeeper was killed on Sunday.
France, a key player in Lebanon, called for an urgent UN Security Council meeting, which was subsequently scheduled for Tuesday at 1400 GMT.
Economy ministers and central bankers from the G7 club of rich countries, meanwhile, met in Paris to discuss the war's consequences, with many countries introducing energy-saving measures.
Market experts warned that any US ground operation or wider Iranian retaliation could send oil prices to levels not seen since the 2008 commodity boom.
* This story was edited by Ahram Online.
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