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Mining, oil stocks help Europe higher; Greece up 11%

European equities closed higher Tuesday, thanks to a rally in the energy and basic resources sectors and a degree of relief over Greece's latest plans to renegotiate its debt.

BP shares rise

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The pan-European Euro Stoxx 600 Index ended the day higher with heavily-weighted stock BP helping the wider benchmarks. Shares were up 2.5 percent after the company reported a narrow loss for its fourth quarter and announced a cut to its capital expenditure plans. The price of oil also rose Tuesday, further helping the beleaguered sector.

Read MoreBP's Dudley: Oil may stick at $50 'for some time'

"We believe that BP has put on fantastic performance and dividend announcement by the company was a brave move, especially if you look at the price of oil, which is down nearly 56 percent from its peak," Naeem Aslam, the chief market analyst at Avatrade, said in a morning note.

Meanwhile, mining stocks with exposure to Australia surged higher. Shares of BHP Billiton rose 4.7 percent and Rio Tinto climbed 3.5 percent. The Reserve Bank of Australia cut rates on Tuesday for the first time since August 2013 as it attempts to support an economy hit by falling commodity prices.

Read MoreBP hit by $3.6B charge, cuts capex on oil prices

Greece deal?

Greece's Finance Minister Yanis Varoufakis unveiled proposals on Monday to end the confrontation with its creditors by swapping outstanding debt for new growth-linked bonds, the Financial Times reported. The country's finance minister continues his charm offensive around Europe to drum up support for a new debt deal. On Tuesday, Varoufakis is due to meet with Italian Finance Minister Pier Carlo Padoan in Rome.

Greek stocks were up 11 percent on Tuesday, after showing heavy losses last week, with investors cheering the possibility of the new deal.

Meanwhile in the U.S, equity markets were in buoyant mood, with the Dow Jones average up 1 percent and the broader S&P 500 up by 0.6 percent.

Spain jobs upbeat

On the data front, Spanish jobs data posted its best January since 2007. January is usually a poor month for employment but seasonally adjusted claims fell by 42,723 people, according to the Spanish labor ministry.

Read MoreSpain's jobless posts best January since 2007

In other stocks news, Danske Bank shares rose 1.5 percent as the lender launched a buy-back scheme and posted better-than-expected profit.

Shares of Banco Santander climbed 4 percent it posted a 70 percent profit jump in the last quarter of 2014.

Meanwhile, Aberdeen Asset Management lost 3 percent after announcing a fall in funds under management.

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