US and European stock markets rebounded and oil prices tumbled Tuesday on easing fears of an imminent Russian invasion of Ukraine.

Russia raised hopes of a de-escalation of tensions with the West as it announced it was pulling back some of the troops deployed on Ukraine's border.

Western leaders applauded the statement, but called for verification. US President Joe Biden said that a Russian attack on Ukraine remains "very much" a possibility, but that a diplomatic solution to the crisis could yet be reached.

US and European equities moved unambiguously higher, with major Wall Street indices winning 1.2 percent or more after Paris and Frankfurt both added about two percent.

"While risks remain elevated, this looks like a big step in the right direction, and investors, like everyone else, are breathing a huge sigh of relief," said Craig Erlam, senior market analyst at foreign exchange broker OANDA.

The Russians "said they were going to pull troops back but nobody said they have actually seen them pulling troops back," said LBBW's Karl Haeling.

"But sometimes the market knows what's going on and the fact that crude oil sold off as much, people have the feeling beyond those official statements that they really aren't going to go in."

In addition to fears about a possible war in Eastern Europe, investors have been concerned about the US Federal Reserve possibly taking a more aggressive stance on interest rates to tame inflation.

But US stock markets shrugged off government data showing that the producer price index rose one percent, seasonally adjusted, in January -- twice what analysts had forecast.

"Many economists are hoping this is peak inflation and the economy will start to turn around soon, but reports have been consistently hotter each month since October," said TD Ameritrade chief market strategist JJ Kinahan.

The easing tensions over Ukraine also weighed on commodity prices.

Oil prices, which have shot to seven-year highs during the Ukraine crisis, tumbled as much as four percent in value. Russia is a major exporter of both oil and natural gas.

Wheat prices also cooled on Tuesday. Russia and Ukraine are major producers and exporters of the commodity.

In earlier Asian stock market trading, Tokyo retreated as investors brushed off data showing Japan's economy rebounded in the final three months of 2021.

There were losses also in Hong Kong, Sydney, Singapore, Seoul, Wellington, Taipei and Manila, but Shanghai, Mumbai, Bangkok and Jakarta edged up.

German Chancellor Olaf Scholz is due in Moscow for talks with Vladimir Putin on Tuesday to try to find a diplomatic route out of the crisis in Ukraine
German Chancellor Olaf Scholz is due in Moscow for talks with Vladimir Putin on Tuesday to try to find a diplomatic route out of the crisis in Ukraine AFP / Sergei SUPINSKY

New York - Dow: UP 1.2 percent at 34,988.84 (close)

New York - S&P 500: UP 1.6 percent at 4,471.07 (close)

New York - Nasdaq: UP 2.5 percent at 14,139.76 (close)

London - FTSE 100: UP 1.0 percent at 7,608.92 (close)

Frankfurt - DAX: UP 2.0 percent at 15,412.71 (close)

Paris - CAC 40: UP 1.9 percent at 6,979.97 (close)

EURO STOXX 50: UP 2.0 percent at 4,143.71 (close)

Tokyo - Nikkei 225: DOWN 0.8 percent at 26,865.19 (close)

Hong Kong - Hang Seng Index: DOWN 0.8 percent at 24,355.71 (close)

Shanghai - Composite: UP 0.5 percent at 3,446.09 (close)

West Texas Intermediate: DOWN 3.6 percent at $92.07 per barrel

Brent North Sea crude: DOWN 3.3 percent at $93.28 per barrel

Euro/dollar: UP at $1.1361 from $1.1307 late Monday