London (AFP) - Europe's main stock markets rallied Tuesday, recording a second day of gains on hopes of a deal being struck on Greece's debt, with a rebound in oil prices helping energy shares.The Greek stock market soared by more than 11.3 percent after Athens elaborated on its plans that would see repayment of its huge international bailout loans delayed but avoid a politically sensitive write-off of the debt.London's FTSE 100 rose 1.32 percent to 6,871.80 points, in Paris the CAC 40 rose 1.09 percent to 4,677.90 points, and Frankfurt's DAX 30 index climbed 0.58 percent to a record high close of 10,890.95 points.Madrid spiked 2.32 percent higher and Milan 2.57 percent.The euro leapt to $1.1456 from $1.1343 late in New York late on Monday."Global equity markets extended gains in today's trading session and climbed higher following a strong rebound in crude oil prices and as concerns regarding Greece’s uncertainty eased," said analyst Myrto Sokou at Sucden Research.Greece's new anti-austerity leaders flew into Rome on Tuesday to build support for new proposals aimed at ending a stand-off with the country's eurozone partners which footed the bill for the country's bailout.In an interview with the Financial Times, Greek Finance Minister Yanis Varoufakis said the leftist-dominated government in Athens would be making proposals for "a menu of debt swaps" that would avoid the need for any of the country's mountain of foreign debt to be written off."Greece's problems are far from over but as far as the markets are concerned calm has been restored," said David Madden, market analyst at IG trading group. - Oil helps energy stocks - On the corporate front Tuesday, the energy sector won support from signs of recovery in the oil market."The bounce in oil has boosted shares in the commodity sector and this theme could continue for some time yet," noted Fawad Razaqzada, analyst at Forex.com."Oil prices have rebounded strongly over the past three trading sessions on signs that producers are cutting back output." European benchmark Brent North Sea crude for delivery in March jumped $1.20 to $55.94 per barrel in late London trading, while West Texas Intermediate (WTI) for March won $1.15 to $50.72.Shares in BP jumped by 2.78 percent to 449.85 pence, lifted also by better-than-expected earnings revealed by the British energy group. The company meanwhile joined sector peers in announcing that it plans to slash investment this year as the recent plunge in crude prices bites into group profits. Spending in 2015 was expected to total about $20 billion, down from a previous guidance of $24-26 billion, BP said in a results statement.And smaller British rival BG Group revealed it would cut investment by about $3.0 billion this year.Royal Dutch Shell gained 5.36 percent to 2,180.00 pence, and Tullow Oil climbed 4.61 pence.In Paris, shares in Total rose 2.72 percent to 48.28 euros. - Australia shines on miners - Mining stocks benefitted from Australia's central bank cut interest rates to a record low 2.25 percent, which sent the Aussie dollar lower.Shares in Glencore soared 6.42 percent to 269.35 pence and BHP Billiton gained 5.02 percent to 1,558.50 pence. Shares in Anglo American climbed 4.09 percent to 1,170.00 pence and Rio Tinto climbed 3.88 percent to 3,076.00 pence."Mining companies including BHP Billiton and Rio Tinto with large Australian operations benefited from an overnight rate cut from the Reserve Bank of Australia which sent production costs tumbling alongside the Australian dollar," said analyst Jasper Lawler at CMC Markets UK.Shares on Wall Street pushed higher on Tuesday, following European equities upward on optimism for a deal to renegotiate Greece's debt.The Dow Jones Industrial Average rose 0.80 percent to 17,499.15 points in midday trading.The broad-based S&P 500 climbed 0.65 percent to 2,034.06, while the tech-rich Nasdaq Composite Index added 0.18 percent to 4,685.16.In Asian trading, Sydney stocks surged 1.46 percent higher on Australia's central bank interest rate cut.Tokyo sank 1.27 percent owing to a pick-up in the yen against the dollar.Hong Kong added 0.29 percent and Shanghai rallied 2.45 percent on expectations of some policy easing after weak manufacturing figures from China on Sunday and Monday.Seoul ended flat.Join the conversation about this story »