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Global markets have rallied on hopes that military tensions over Ukraine could ease after Russia said it was recalling some of its troops from the country's border.
Exchanges in Italy and Germany closed nearly 2% higher and French markets climbed 1.6% while London's FTSE 100 gained 1%.
The three major US indexes also jumped more than 1% at the open.
Western officials greeted news of the development with caution.
Markets had slumped on Monday after the US warned that Russia could invade Ukraine at any time.
Nato on Tuesday said Russia's troop announcement gave cause for "cautious optimism" but warned that it had not seen evidence of de-escalation on the ground.
Russia has always denied it was preparing for invasion.
The market rally comes after concerns about the conflict prompted a sell-off.
The FTSE 100 plunged 1.7% on Monday, its worst session in three weeks, led by shares in travel companies, among the firms most exposed should Western sanctions on Russia or a war lead to higher oil prices.
On Tuesday, oil prices retreated, falling more than 4% at one point.
In the US, aeroplane maker Boeing was the biggest winner on the Dow, up more than 3%. Travel companies, such as Expedia, United Airlines and American Airlines, helped power the rally on the S&P 500.
The gains came despite new data showing worse-than-expected increases in producer prices, which could lead the Federal Reserve to move more aggressively to combat inflation.
In London, AstraZeneca led the market gains, rising more than 5% after saying it had seen positive results in trials for a drug in development, while mining giant Evraz, which has operations in Russia, was also up more than 4%.
German Chancellor Olaf Scholz and Russian President Vladimir Putin met on Tuesday and discussed the Nord Stream 2 gas pipeline, which has been completed but not approved to open amid stiff opposition from the US and some European states.
In comments at a press conference following the meeting, Mr Scholz said Germany was committed to ensuring that transit of gas works according to "according to the agreements we have," he said.
He added: "We also want to ensure peaceful development in Europe, that there will be no military confrontation in Ukraine. If that is the case, it will have far-reaching consequences."