With both the American and European economies in a fragile state, US President Barack Obama has warned that their economies would continue to be at risk until European leaders work together to solve their debt problems.In a rare public expression of criticism aimed at America's transatlantic allies, US President Barack Obama has called on European leaders to develop a "more effective set of coordinated policies" to deal with the continent's sovereign debt crisis."Right now you have a single currency, but you don't have a single set of economic policies, and that's created great difficulty," Obama said in reference to the eurozone. "It's difficult to coordinate when you have that many countries with different politics and different economic situations trying to agree on a common course."Speaking to a group of Hispanic journalists at the White House on Monday, Obama said Greece was "obviously the biggest immediate problem" and that the government there was "taking some steps to slow the crisis but not solve the crisis."The bigger problem is what happens in Spain and Italy if the markets keep on making a run at those very big countries," he added, saying Washington was "deeply engaged" with European nations on how to solve the eurozone crisis.US Treasury Secretary Timothy Geithner, meanwhile, plans to attend a meeting of eurozone finance ministers later in the week. Geithner just returned to the US from Marseilles, France, where he called on Europe's largest economies to offer "unequivocal" financial support for weaker economies such as Greece.It would be the first time in history that a US treasury secretary has attended a meeting of eurozone finance ministers, highlighting the concern Washington has over Europe's handling of the sovereign debt crisis.US stocks, meanwhile, closed higher on Monday after recovering from a short dip of 1 percent earlier in the day. These gains led to positive numbers in Asian markets, with the euro edged up from a seven-month low on Tuesday.World markets and the euro made slight gains on Tuesday as confidence was bolstered by the late rally in the United States, while news of possible financial support for Italy from China did little to ease fears that the eurozone was on the brink of disaster.A report by the Financial Times said Italy, whose mammoth debt has investors worried it may eventually need a bailout like Greece, Ireland and Portugal, had asked China to make "significant" purchases of Italian bonds.The possibility of support from China would be good news for Italy, which has seen borrowing costs skyrocket in recent months. But the biggest problem in the eurozone remains Greece, which said it would run out of cash next month without the next installment of bailout funding from the European Union and the International Monetary Fund.European stock markets tumbled Monday after German politicians talked openly of the possibility of Greece defaulting on its debt and leaving the eurozone. As trading ended Germany's DAX was still down over 2 percent - following a disastrous showing last Friday, and a distinct downward trend in Frankfurt over the past six weeks.Greece has resumed talks with international lenders to receive its next 8-billion-euro ($11 billion) installment of aid in order to avert a default on its debt as the national government in Athens runs dangerously low on cash. Talks had been suspended over criticism that Greece had not been taking strong enough measures to restructure its economy and reduce public deficits in exchange for the bailout money. Athens approved a new real estate tax on Sunday to try to shore up its budget.Greece's second bailout of nearly 110 billion euros, approved during a eurozone crisis summit in July, has run into difficulty as governments in northern Europe become increasingly skeptical of Athens' seriousness in tackling its economic problems.Finland has demanded collateral from Greece in exchange for its contribution to the bailout. Germany's Christian Social Union, the sister party of Chancellor Angela Merkel's conservative Christian Democrats, has publicly floated the possibility that Greece could leave the eurozone.Germany's Economy Minister Philipp Rösler, meanwhile, wrote in a Monday editorial in the daily Die Welt that the eurozone would have to remain open to the possibility of a "worst-case scenario orderly default for Greece."