A screen shows Nikkei index after a ceremony marking the end of trading in 2021 at the Tokyo Stock Exchange (TSE) in Tokyo, Japan December 30, 2021.
A screen shows Nikkei index after a ceremony marking the end of trading in 2021 at the Tokyo Stock Exchange (TSE) in Tokyo, Japan December 30, 2021. Reuters / KIM KYUNG-HOON

Stocks on Wall Street and in Europe rebounded on Tuesday while oil prices fell after Russia indicated it was withdrawing some troops from exercises near Ukraine and President Vladimir Putin said he saw room for further discussion with the West.

President Joe Biden later said a Russian attack on Ukraine remained possible and that the United States would defend every inch of NATO territory.

Gold and bond prices slid as safe-haven assets lost some of their appeal with tensions possibly easing over Ukraine. But NATO said it had yet to see any evidence of de-escalation and a vote in Russia's lower house threatened a wider standoff.

The State Duma agreed to ask Putin to recognize two Russian-backed breakaway regions in eastern Ukraine as independent, a move the European Union told Moscow not to adopt.

The dollar index pared losses as Putin and German Chancellor Olaf Scholz spoke, a sign tensions over Ukraine have not been resolved. But the index fell 0.294%, suggesting there was little flight to safety, especially as the euro, which had weakened recently, rose 0.44% to $1.1355.

The Russian ruble strengthened 1.53% at 75.51 per dollar.

"In the back of everybody's minds this is not going away. Putin might be saying one thing and just waiting for the right time to make a move," said Tom di Galoma, managing director at Seaport Global Holdings.

Major stock indices rose on both sides of the Atlantic, with megacap growth and tech stocks leading the rally on Wall Street. The major European bourses posted gains of more than 1%.

The pan-European STOXX 600 index rose 1.43% after falling three consecutive sessions, while MSCI's U.S.-centric gauge of global equities closed up 1.34%.

On Wall Street, the Dow Jones Industrial Average rose 1.22%, the S&P 500 added 1.58% and the Nasdaq Composite advanced 2.53%.

While the Ukraine crisis simmered, the Labor Department reported U.S. producer prices increased by the most in eight months in January, a reminder that high inflation could persist through much of this year.

The Federal Reserve is aware inflation is running hot but knows rising home prices and mortgage rates will crimp the pocket book of many Americans, leading the economy and inflation to slow, said Peter Cramer, senior managing director at SLC Management.

"They know they have to get inflation under control, but the slowing of economic activity that will really help do that is already starting to happen," Cramer said.

A closely watched part of the yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations, is starting to signal a sharp slowdown, as it flattens to 47.1 basis points.

The odds of the Fed engineering a recession are increasing if policymakers do not push back against a market narrative of six or so interest rate hikes in a row, Cramer said.

It remains to be seen whether the Fed can get inflation under control by raising interest rates alone, di Galoma said.

Markets are pricing in a 65.5% chance of a 50-basis-point hike and a 34.5% chance of a 25-bps hike at the U.S. central bank's March meeting.

Longer-dated U.S. Treasury and euro zone bond yields rose, as investors took comfort from the potential easing of tensions over Ukraine and essentially ignored the PPI data.

The benchmark 10-year Treasury note rose 5.6 basis points to 2.052%. Germany's 10-year yield touched its highest since 2018 on the day's possible easing of Russia-Ukraine tensions.

Oil prices tumbled more than 3% as they retreated from a seven-year high.

U.S. crude futures fell $3.39 to settle at $92.07 a barrel, while Brent futures settled down $3.20 at $93.28 a barrel.

Precious metals also fell, with gold slipping from a multi-month high and palladium shedding more than 5%.

U.S. gold futures settled down 0.7% at $1,856.20 an ounce.

Bitcoin rose 4.33% to $44,066.83 in another sign of the risk-on mood in markets.