Europe's failure to tackle crippling Greek debt is "scaring the world," US President Barack Obama warned as Germany rejected plans to boost funding for the EU's debt rescue facility. Asian stocks rallied sharply Tuesday, following a see-sawing recovery on US and European markets as investors absorbed mixed messages over how the eurozone intends to chart its way out of the debt crisis. Speculation over a more ambitious bailout fund and an orderly Greek default sent Tokyo stocks up 2.82 percent by the close, while Seoul soared 5.02 percent and Hong Kong added more than three percent by mid-session. Asian markets were also looking ahead to a meeting later Tuesday between German Chancellor Angela Merkel and Greek Prime Minister George Papandreou when they will discuss the Greek economy and the reforms by Athens. However, the euro came under renewed pressure against the dollar in Asian trade on Tuesday, resuming its fall after a brief respite overnight. Europe "never fully dealt with all the challenges that their banking system faced," Obama said Monday. "It's now being compounded with what's happening in Greece," he said. "So they're going through a financial crisis that is scaring the world." US Treasury Secretary Timothy Geithner also urged Europe to step up its response to the crisis, after a round of meetings involving the World Bank IMF and G20 since last Thursday. "They recognized the need to escalate. They're going to have to put a much more powerful financial framework behind this," Geithner told ABC News. "I really believe that you're going to see them do that, but we wanted to make sure they do it as quickly as they can and as definitively as they can." Germany on Monday hosed down a push to expand a stability fund designed to quarantine the eurozone in the event of an escalating crisis, and fend off the threat of a global double-dip recession. Economic Affairs commissioner Olli Rehn had said earlier that the 440-billion-euro ($590 billion) European Financial Stability Facility, the cornerstone of a second Greek bailout, should be given "greater strength." His spokesman Amadeu Altafaj added that discussions following intense debt diplomacy in Washington were now centred on an "increase of the means at the EFSF's disposal." However, German Finance Minister Wolfgang Schaeuble insisted there was no plan to boost the fund's warchest. "We are giving it the tools so it can work if necessary," Schaeuble said, referring to the new powers allowing the fund to lend to countries such as Italy even before they hit cashflow crises. "Then we will use it effectively -- but we do not have the intention of boosting its volume," he said. Schaeuble's blunt reaction comes ahead of a parliamentary vote in Germany Thursday to ratify earlier changes to the fund's operating scope, agreed in principle in July. Germany is continental Europe's de facto paymaster, expected to provide the lion's share of any increased loans, but German Chancellor Angela Merkel is facing increasing discontent inside her own party. Schaeuble's intervention slowed the momentum built up during intense debt diplomacy in Washington over the weekend. There, the International Monetary Fund, the United States and other G20 economies pushed Europe to ring-fence the really big risks such as Italy -- in a concerted effort to prevent the world slipping into a fresh downturn. "We are thinking about the possibility of giving the EFSF greater leverage, to give it greater strength," Rehn had said. But just eight of the 17 eurozone states have so far ratified the new EFSF powers agreed at a July summit, which also opted for a 159-billion-euro successor to last year's failed 110-billion-euro Greek rescue. The fund has already been tapped by Ireland and Portugal, so investors want to be convinced that Italy will not need help further down the line. Germany opposes any increase in the size of the government "guarantees" that give the EFSF its borrowing clout. The hope for non-European leaders is that Berlin might back an alternative measure enabling the fund to raise more "capital," in the interests of wider financial stability. Speculation suggests the fund's reach, even on the same guarantees, could ultimately stretch as high as three trillion euros. Austrian Finance Minister Maria Fekter said however that taxpayers should be spared any further pain, and politicians in Slovakia are blocking the measure. Greece meanwhile is still waiting for a date for the return of EU and IMF auditors, which means eight billion euros in blocked loans may now have to be considered by EU leaders at an October 17-18 summit in Brussels. Greece has yet to convince its creditors it can fix the hole in its finances, or successfully implement the state sell-offs its bailout partners are insisting on, before a cashflow crunch in mid-October.