Optimism over Washington's proposal to Iran to ease the conflict collapsed when Trump told reporters on Monday that Iran's counter-offer was "garbage".

Trump warned that Tehran's rejection of his administration's demands meant the already tenuous ceasefire is now "unbelievably weak".

The impasse, which leaves the vital Strait of Hormuz mostly closed to oil tanker traffic, unnerved global energy markets.

The international benchmark Brent crude price jumped one percent to US$105 a barrel during Tuesday morning trade in Asia, while benchmark US oil contract West Texas Intermediate (WTI) also rose one percent to $99 a barrel.

Precious metals also increased, with silver surging more than eight percent to $87 an ounce, capping weeks of rising prices.

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But markets were mostly subdued, as analysts reported that traders are in wait-and-see mode as the 10-week war drags on.

"For now, President Trump is still talking about the idea that the ceasefire is on a 'massive life support'," analyst Rodrigo Catril told the NAB Morning Call podcast, referring to the US president's comments to reporters on Monday.

"The theme, I think, for markets is that as much as President Trump is not happy with what is on offer, he's also not suggestng that there's going to be an escalation."

US stocks held modest gains in Monday's trade, finishing a meandering session modestly higher as enthusiasm about artificial intelligence managed to offset concerns about higher oil prices.

South Korea's tech-rich Kospi rose one percent in early trading, but later plunged to erase its opening gains.

But analysts have warned oil prices could spike dramatically if the war drags on into June as crude supplies dwindle.

"Beneath the surface calm sits a market increasingly dependent on the assumption that the Strait of Hormuz will gradually reopen sometime before late June," said Stephen Innes, analyst with SPI Asset Management.

"An extended disruption (to the strait) would almost certainly force oil prices materially higher, tighten global financial conditions, and inflict far more serious economic damage than markets currently price in," he said.

Traders were also looking to Japan, where US Treasury Secretary Scott Bessent arrived on Monday to discuss matters including currency issues, the Nikkei daily reported.

The visit comes ahead of Trump's trip to China this week, where top executives including Tesla boss Elon Musk and Apple's Tim Cook will join the US president to push US hopes to ramp up trade.

The war with Iran will also top the agenda, with Trump expected to press President Xi Jinping -- a major buyer of Iranian oil, according to a senior US official.

Iranian officials will be keeping a close eye on Trump's visit to Beijing, which has quietly engaged in efforts to resolve the crisis.

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