Iran showed no sign of agreeing to US President Donald Trump's ultimatum to open the Strait of Hormuz ​by the end of Tuesday or face bombing of civilian infrastructure in what would be the biggest escalation yet of the war.

As the clock ticked down on Trump's deadline to unleash "hell", strikes on Iran ‌intensified throughout the day, hitting railway and road bridges, an airport and a petrochemical plant and knocking out power lines, according to Iranian media.

Iran responded by declaring it would no longer hold back from hitting infrastructure of its Gulf neighbors, and claimed to have carried out fresh strikes on a ship in the Gulf and Saudi industrial facilities linked to US firms.

A senior Iranian source told Reuters that Tehran had rejected a proposal conveyed by intermediaries for a temporary ceasefire. Talks on a lasting peace could begin only after the US and Israel end their strikes, provide ​a guarantee they will not resume and offer compensation for damages.

Any future settlement must leave Iran in control of the strait, imposing fees on ships that use it, the source said on condition of anonymity.

Trump has given ​Iran a deadline of 8 p.m. in Washington (midnight GMT and 3:30 a.m. in Tehran) to end its blockade of Gulf oil, saying he will otherwise destroy every bridge and power plant in Iran ⁠within four hours. Iran says it would retaliate against infrastructure of US allies in the Gulf, whose desert cities would be effectively uninhabitable without power or potable water.

Yet despite the intensification of strikes on the ground and rhetoric from both sides, global ​markets were largely frozen, hesitant to bet on whether Trump would follow through on his threats or call them off as he has in the past.

Strikes on bridges, power lines, airport

Among the reported strikes inside Iran throughout the day were attacks on railway ​bridges, a highway bridge, a petrochemical plant and an airport. Power was knocked out in parts of Karaj just west of Tehran by a strike on transmission lines and a substation. Explosions were reported on Kharg Island, site of Iran's main oil export terminal which Trump has publicly mused about destroying or seizing.

Israel warned Iranians in a Persian-language social media post to stay away from trains, saying anyone near railways would be in danger.

A synagogue in Tehran was destroyed overnight by Israeli air strikes. Footage in Iranian media showed Hebrew texts ​scattered in the debris.

"The synagogue building was completely destroyed and our Torah scrolls were left under the rubble," said Homayoun Sameh, a lawmaker who represents Iran's Jewish community, one of the Middle East's largest outside Israel. Israel's military had no immediate ​comment.

Iran's Revolutionary Guards said in a statement that Tehran's response would "deprive America and its allies in the region of oil and gas for years."

"America's regional partners should know that up to today we have shown great restraint for the sake of good neighborliness and have ‌had some consideration ⁠in choosing targets for retaliation," it said. "But all these considerations have since been removed."

Wish for another bluff

Iranians hoped the threatened escalation could be averted.

Trump has abruptly called off similar threats over the past several weeks, citing what he has described as productive negotiations with unidentified figures in Iran, though Tehran has denied any substantive talks have taken place.

The two countries have so far exchanged proposals, with Pakistan acting as the main go-between, but there has been no sign ​of compromise, with both sides claiming to have won the ​war and demanding concessions to end it.

Iran's ambassador to ⁠Pakistan said Tuesday that "positive and productive endeavors" by Islamabad to mediate an end to the war were "approaching a critical, sensitive stage", but gave no further details.

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A proposal brokered by Pakistan would call for a temporary ceasefire and the lifting of Iran's effective blockade of the strait, while putting off a broader peace settlement for further talks, according to a source familiar with ​the plan.

But Iran's 10-point response, as reported by IRNA news agency on Monday, would require a permanent end to the war, the lifting of sanctions and a promise of ​the reconstruction of Iranian sites damaged ⁠by the Israeli-US strikes.

It would also include a new mechanism to govern passage through the Strait of Hormuz – previously an open international waterway through which a fifth of global oil and liquefied natural gas typically passed. Since the United States and Israel attacked Iran on February 28, Iran has effectively closed it to nearly all ships apart from its own.

Trump imposed his latest deadline on Iran in a social media message on Sunday, using language Iranian officials ​described as desperate or even mad.

At a press conference on Monday, Trump doubled down: "Every bridge in Iran will be decimated," he threatened. "Every power plant in ​Iran will be out of business, burning, exploding, and never to be used again."

Iran's envoy to the United Nations said Trump's threats were "direct incitement to terrorism and provide clear evidence of intent to commit war crimes under international law." Its top military command said Trump was "delusional."