Oil edges up and equities mixed amid mixed messages on 'talks'
But while crude prices are down from last week and the mood on trading floors has been less dour than most of March, uncertainty and the virtual closure of the Strait of Hormuz -- through which around 20 percent of oil and gas passes -- continues to cast a dark shadow.
Washington presented a 15-point plan to end the war, including Iran giving up its enriched uranium and opening up the waterway, while Tehran's state-run TV reported officials had put forward their own five conditions for hostilities to end.
Trump on Wednesday threatened to "unleash hell" if Iran did not strike a deal, but Foreign Minister Abbas Araghchi said his country does not intend to negotiate.
However, the US president also said Iran was taking part in peace talks and the denials were because negotiators feared being killed by their own side.
"Pressure on energy prices, shipping flows and broader financial conditions remains one of the few meaningful sources of leverage (Iran) retains," said Saxo Markets' Charu Chanana.
"There is therefore little incentive to relinquish that leverage prematurely, particularly if market stress strengthens its negotiating position.
However, she added: "It would be imprudent to assume diplomacy is absent simply because it is not visible. In conflicts of this nature, public rhetoric and private negotiation often diverge materially.
"Markets understand this dynamic, and they also tend to inflect before the political endgame is formally in place."
With investors holding on to hope that a deal can be struck, oil prices have stabilised this week, with Brent sitting just above $100 and WTI around $90.
Equities were also less volatile.
After gains on Wall Street and Europe, Asian markets fluctuated after a two-day rally.
Tokyo, Hong Kong, Shanghai, Seoul, Manila and Jakarta fell.
Singapore, Wellington and Taipei rose, while Sydney was flat.
But City's Index's Fiona Cincotta said: "For the recovery to gain more meaningful traction, investors will want to see clearer signs of de-escalation, including the reopening of the Strait of Hormuz."
Her remarks come after the head of the International Chamber of Commerce, John Denton, warned the conflict could cause the "worst industrial crisis" in decades.
"The head of the International Energy Agency has warned that the world is facing an energy crisis more severe than the oil shocks of the 1970s," he added.
"From a business perspective, we believe this could yet become the worst industrial crisis in living memory."
Meanwhile, the World Trade Organization said disruptions to fertiliser supplies posed a double threat to global food security through scarcity and high prices, with a third of the global fertiliser supply normally transiting the Strait of Hormuz.
Key figures at around 0230 GMT
West Texas Intermediate: UP 1.2 percent at $91.41 a barrel
Brent North Sea Crude: UP 1.0 percent at $103.25 a barrel
Tokyo - Nikkei 225: DOWN 0.2 percent at 53,658.47 (break)
Hong Kong - Hang Seng Index: DOWN 1.3 percent at 25,004.70
Shanghai - Composite: DOWN 0.4 percent at 3,916.10
Euro/dollar: DOWN at $1.1560 from $1.1565 on Wednesday
Pound/dollar: DOWN at $1.3353 from $1.3365
Dollar/yen: UP at 159.49 yen from 159.47 yen
Euro/pound: UP at 86.57 pence from 86.52 pence
New York - Dow: UP 0.7 percent at 46,429.49 (close)
London - FTSE 100: UP 1.4 percent at 10,106.84 (close)