Global stocks rallied and oil prices fell Wednesday after US President Donald Trump said the Middle East war that has roiled markets could be over within weeks.
Wall Street's main indices were higher in midday trading, building on a rally from the previous day.
In Europe, Frankfurt and Paris both jumped more than two percent, while London rose 1.9 percent.
That came after Asian markets closed sharply higher, with Seoul soaring more than eight percent, Tokyo up five percent and Chinese stocks also rising.
Trump said Tuesday the United States would end operations in Iran "very soon", perhaps within "two weeks, maybe three".
The White House said he would address the nation on Wednesday "to provide an important update on Iran".
"Markets still seem to be betting on a resolution to the war and a reopening of the Straits of Hormuz," said Chris Beauchamp, chief market analyst at online trading platform IG.
Oil prices fell, with international benchmark Brent down one percent after falling as much as five percent earlier. The main US contract WTI dropped two percent.
The economic impact of the conflict is worsening, with average US gasoline prices topping $4 a gallon for the first time in four years this week, European inflation spiking and governments unveiling a range of support measures.
Iranian President Masoud Pezeshkian said the Islamic republic had the "necessary will" to end the war, provided its enemies guaranteed it would not flare up again.
But Israeli Prime Minister Benjamin Netanyahu insisted that Israel would press ahead with its military campaign and that "we will continue to crush the terror regime".
Traders remained wary as fresh strikes hit Tehran on Wednesday, and an oil tanker off the coast of Qatar was hit by an Iranian missile.
Trump said Wednesday that Iran has asked for a ceasefire but that the United States wants the Strait of Hormuz to be clear for shipping.
Iran's Revolutionary Guards insist that the strategic strait will remain closed to the country's "enemies".
"Despite today's relief wave on markets, deep problems remain," said Susannah Streeter, chief investment strategist at Wealth Club.
She said that elevated crude prices, still about 50 percent above pre-war levels, "signals that scepticism still remains about Trump's claims of progress, and worries persist about how extraction from the conflict is still set to be complex".
FOREX.com analyst Fawad Razaqzada noted that the head of the International Energy Agency had signalled that some 12 million barrels per day of oil production has been disrupted, leading to shortages of jet fuel and diesel.
"It’s clear why oil isn’t collapsing despite the market’s attempt to lean into de-escalation," he said.
"There’s simply too much uncertainty, both in terms of supply disruption and geopolitical escalation, for prices to meaningfully reset lower just yet," added Razaqzada.
IG's Beauchamp noted supply problems haven't yet begun to bite in Europe.
"Optimism might well be misplaced once the real impact starts to become clear," he said.
In company news, shares in Chinese artificial intelligence startup Zhipu, which went public in January, soared more than 32 percent after it said revenue from its cloud business almost tripled last year.
- Key figures at around 1530 GMT -
New York - Dow: UP 0.8 percent at 46,721.42 points
New York - S&P 500: UP 0.9 percent at 6,585.52
New York - Nasdaq Composite: UP 1.3 percent at 21,877.34
London - FTSE 100: UP 1.9 percent at 10,364.79 (close)
Paris - CAC 40: UP 2.1 percent at 7,981.27 (close)
Frankfurt - DAX: UP 2.7 percent at 23,298.89 (close)
Tokyo - Nikkei 225: UP 5.2 percent at 53,739.68 (close)
Hong Kong - Hang Seng Index: UP 2.0 percent at 25,294.03 (close)
Shanghai - Composite: UP 1.5 percent at 3,948.55 (close)
Brent North Sea Crude: DOWN 2.4 percent at $101.46 a barrel
West Texas Intermediate: DOWN 2.2 percent at $99.14 a barrel
Euro/dollar: UP at $1.1610 from $1.1551 on Tuesday
Pound/dollar: UP at $1.3321 from $1.3236
Dollar/yen: DOWN at 158.61 from 158.77 yen
Euro/pound: DOWN at 87.16 pence from 87.28 pence
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