World oil prices surged to new multi-year peaks on Tuesday, extending a bullish run one day after OPEC+ refrained from boosting output any further.

The news handed a boost to share prices of energy firms while European and US stock markets rebounded from losses a day earlier.

But Asia equities fell on concerns that soaring energy prices would further fuel inflation.

European benchmark London Brent North Sea oil jumped to a new three-year peak at $83.13 per barrel.

New York crude hit a fresh seven-year pinnacle at $79.48.

OPEC and other major producers opted on Monday against increasing output by more than previously agreed -- despite tightening supplies and rising demand.

The OPEC+ grouping decided to stick with their planned increase next month in oil production of 400,000 barrels.

Red rag

"OPEC+ gave oil bulls a red rag to bid up futures contracts as it stuck to the planned increase," said Markets.com analyst Neil Wilson.

"It's not that demand is suddenly forecast to improve -- it's more that OPEC+ is keeping such a tight grip on supply."

Higher oil prices fuel inflation but boost the profits and revenues of energy giants.

In London, BP shares rose 1.8 percent to 351 pence and Royal Dutch Shell's 'B' shares jumped 2.2 percent to £17.07.

In Paris, France's TotalEnergies soared 3.0 percent to 43.36 euros, and in New York shares in ExxonMobil climbed 0.8 percent to $62.20.

"OPEC's decision not to lift production volumes gave oil prices a lift into Tuesday, helping the FTSE 100 to solid gains as index heavyweights BP and Shell gushed higher," said AJ Bell investment director Russ Mould.

Wall Street rebounded at the start of trading, shaking off losses on Monday 

"US stocks are rebounding as investors find value in beaten up tech stocks and are coming to the realisation that the global natural gas crisis is good news for energy stocks," said analyst Edward Moya at currency trading platform Oanda.

But "it remains to be seen whether the bulls will be able to hold their ground in the face of rising concerns over stagflation," said ThinkMarkets analyst Fawad Razaqzada.

Elsewhere on Tuesday, most Asian markets fell following Wall Street's Monday slump.

Investors were nervously monitoring developments in the crisis surrounding troubled property giant China Evergrande, which has raised warnings about contagion in the world's number two economy and possibly beyond.

Meanwhile, bitcoin bounced above $50,000 for the first time in four weeks.

"Bitcoin is starting to show bullish signs despite whatever risk mode is happening on Wall Street," said Oanda's Moya.

- Key figures around 1530 GMT -

Brent North Sea crude: UP 2.2 percent at $83.08 per barrel

West Texas Intermediate: UP 2.3 percent at $79.48

New York - Dow: UP 1.3 percent at 34,456.67 points

EURO STOXX 50: UP 1.7 percent at 4,064.84

London - FTSE 100: UP 0.9 percent at 7,077.10 (close)

Frankfurt - DAX: UP 1.1 percent at 15,194.49 (close)

Paris - CAC 40: UP 1.5 percent at 6,576.28 (close)

Tokyo - Nikkei 225: DOWN 2.2 percent at 27,822.12 (close)

Hong Kong - Hang Seng Index: UP 0.3 percent at 24,104.15 (close)

Shanghai - Composite: Closed for a holiday

Euro/dollar: DOWN at $1.1609 from $1.1621 at 2100 GMT on Monday

Pound/dollar: UP at $1.3647 from $1.3610

Euro/pound: DOWN at 85.09 pence from 85.38 pence

Dollar/yen: UP at 111.38 yen from 110.93 yen