Europe closed in on a broad agreement Sunday to tackle the euro crisis and pressed Italy to slash its debt mountain to reassure jittery financial markets. European Union leaders came together on the big issue -- over the best approach to take to boost the firepower of a eurozone rescue fund -- but without setting down concrete numbers. France and Germany smoothed out disagreements on how to increase the reach of the 440-billion-euro ($610 billion) European Financial Stability Facility (EFSF). The outcome of back-to-back summits Sunday and this Wednesday is being keenly watched around the world as concerns have grown that the eurozone debt crisis could spark a fresh global recession. There was also agreement to explore a re-opening of the core European Union treaty to cover closer eurozone integration, with a green light for plans to create a Europe-wide budget \'tsar\' -- although non-euro states remain wary about implementation of such measures. Eurozone-only leaders stayed on for further \"technical\" talks Sunday evening but no major statements or press conferences were planned. French President Nicolas Sarkozy said many more \"long hours of talks\" would be needed before nailing down the definitive decisions promised at another EU 27 summit on Wednesday in order to calm nervous financial markets. The second summit in four days was originally meant only to involve the 17 nations that share the euro single currency. It is expected to endorse finance ministers\' calculations that banks will need to be recapitalised to the tune of 108 billion euros ($150 billion). Speaking alongside German Chancellor Angela Merkel at a joint press conference, Sarkozy said \"a quite broad agreement is taking shape on the reinforcement of the EFSF.\" Merkel said a French idea for the fund to acquire a banking licence was dead and buried. That left them looking at plans to offer EFSF insurance to eurozone bond holders, and boost it with top-ups from China and other emerging nations. How to integrate the input of non-European G20 partners waiting for a summit of in Cannes on November 3-4 represented a problem for some, though. Diplomats said offering insurance would lower borrowing rates for the likes of Italy and Spain but no concrete numbers were forthcoming. Just in the last week, officials have revised down the potential reach of a beefed up fund from more than 2.5 trillion euros to 1.0 trillion euros. The \"leveraging\" of the EFSF comes alongside a deal being negotiated with banks for them to accept a 50 percent write-off on Greek debt, in exchange for a new bailout by the EU and the International Monetary Fund. Germany needed for domestic reasons to run any eurozone deal past its parliament\'s budget committee before being able to sign up to any accord. But now non-euro nations led by Britain and Poland also want to see all the small print first to make sure the eurozone is not taking decisions that would affect their interests. Despite the Greek mess, Italy is arguably the bigger concern for all. Italian Prime Minister Silvio Berlusconi came under intense pressure to cut his country\'s deficit and debt. \"We have to reassure investors and reassure other states,\" EU president Herman Van Rompuy said. \"Clearly, we are asking for a major effort on the part of the Italian authorities.\" Italy is carrying debts of 1.9 trillion euros -- equal to 120 percent of what the eurozone\'s third-largest economy produces in a year and way above the EU limit of 60 percent. Merkel too urged \"credible\" cuts in Italy\'s debt as part of efforts to save the eurozone. \"Italy is a great economic force but Italy also has a very high level of debt and it must be reduced in a credible way over the coming years,\" she said. \"That\'s what we expect of Italy.\"