European stock markets rebounded and the euro jumped back above $1.24 Tuesday as investors remained hopeful of central bank action over the eurozone crisis and also cheered Spain\'s latest debt auctions. The benchmark FTSE 100 index of top companies showed a gain of 0.33 percent to 5,843.42 points approaching midday in London. Frankfurt\'s DAX 30 rose 0.39 percent to 7,061.02 points and in Paris the CAC 40 won 0.70 percent to 3,504.90. Milan rallied 1.36 percent and Madrid advanced 0.22 percent. In foreign exchange deals, the euro jumped to $1.2414 from $1.2342 late on Monday in New York. \"European financial markets are firmer today, with stocks, the euro and commodities all grounding higher while Spanish and Italian bond yields continue climbing off dangerous levels,\" said Ishaq Siddiqi, an analyst at ETX Capital. \"Today\'s gains are largely being driven by hopes that the ECB is moving closer to responding with a plan to arrest the spread of the regional debt crisis,\" he added. European stock markets had closed lower on Monday after Germany and the European Central Bank dampened hopes for powerful action to fix the eurozone debt crisis. But markets turned higher Tuesday, helped by news that Spain\'s short-term borrowing costs had tumbled as the eurozone nation raised 4.51 billion euros. The Treasury raised the cash in a sale of 12- and 18-month bills, enjoying a lull in interest rates following ECB chief Mario Draghi\'s comments that the bank may resume bond purchases if necessary. Compared to a similar sale on July 17, the 12-month rate slumped to 3.070 percent from 3.918 percent and the 18-month rate dropped to 3.335 percent from 4.242 percent, Bank of Spain figures showed. Asian stock markets closed mixed on Tuesday amid renewed uncertainty over the eurozone debt crisis after Germany and the European Central Bank dampened hopes for action to drive down borrowing costs despite Draghi\'s comments. Tokyo\'s Nikkei index shrugged off the previous day\'s rally, slipping 0.16 percent as the dollar held on to recent gains against the yen, underlining a continued shift away from the safe haven Japanese currency. German news weekly Der Spiegel on Sunday said the ECB was considering buying bonds issued by heavily indebted eurozone countries in a move that would ensure borrowing costs did not rise beyond a pre-determined level. But an ECB spokesman brushed aside the report as \"absolutely misleading\", while another at the German finance ministry said such an action would \"be very problematic\". Over on Wall Street, US stocks closed flat Tuesday following quiet trading that still though had enough might to push Apple to become the world\'s most valuable company of all time with a total market value of $623.52 billion. That surpassed the previous record of $619 billion set by software titan Microsoft in 1999, during the dot-com boom years.