* Tehran rejects temporary ceasefire, senior Iranian

source says

* Iran says Pakistani mediation efforts at critical stage

* Israel warns Iranians to stay away from trains and

railways

* Deadline approaches on Trump's threat to hit

infrastructure

* Iranian media report strike on synagogue in Tehran

By Parisa Hafezi and Trevor Hunnicutt

DUBAI/WASHINGTON, April 7 (Reuters) - Iran showed no

sign of agreeing to U.S. 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 neighbours, and claimed

to have carried out fresh strikes on a ship in the Gulf and

Saudi industrial facilities linked to U.S. 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

U.S. 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 until 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 U.S. allies in the Gulf, whose desert cities

would be uninhabitable without power or 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 HIT BRIDGES, POWER LINES, AIRPORT

Among the reports of 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 what Iran

described as 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 neighbourliness

and have had some consideration in choosing targets for

retaliation," it said. "But all these considerations have since

been removed."

'I HOPE IT IS ANOTHER BLUFF'

Iranians hoped the threatened escalation could be averted.

"I hope it is another bluff by Trump," Shima, 37, from the

central city of Isfahan, told Reuters by phone. Like many, she

said she wanted the hardline clerical government removed, "but

infrastructure being destroyed and people being unable to build

the future of the country is another matter".

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 on Tuesday "positive and

productive endeavours" by Islamabad to mediate an end to the war

were "approaching a critical, sensitive stage", but gave no

further details.

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-U.S. 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 that declared "Open the Fuckin' Strait, you

crazy bastards, or you'll be living in Hell - JUST WATCH!",

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 U.N. 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."