By David Lawder and Lesley Wroughton

WASHINGTON (Reuters) - The United States and China piled pressure on Europe on Saturday to get to grips with its debt crisis before it risks causing bank runs and pushing the global economy into ruinous recession.

The U.S. Treasury chief, in his most explicit warning to date about the crisis, said it was time for the European Central Bank to step up and take a central role to get it under control.

World financial markets have been wracked by fears the Greek debt crisis could overwhelm other euro zone countries and their banks, but took some comfort on Friday from signs of new resolve by European officials to bolster defenses after nearly two years of what many see as half-hearted action that has policy-makers talking openly of possible Greek default.

"The threat of cascading default, bank runs, and catastrophic risk must be taken off the table, as otherwise it will undermine all other efforts, both within Europe and globally," U.S. Treasury Secretary Timothy Geithner said in a speech at the International Monetary Fund.

"Decisions as to how to conclusively address the region's problems cannot wait until the crisis gets more severe."

Geithner's warning was echoed by China's central bank governor Zhou Xiaochuan, but with an added twist that countries running big deficits, like the United States, also must act responsibly.

"The sovereign debt crisis must be resolved promptly to stabilize market confidence, and forceful and credible fiscal consolidation measures are needed in relevant economies to alleviate sovereign debt stress," Zhou told the IMF.

The semi-annual gathering of the IMF and World Bank is dominated by worry about the risk that Europe now poses to the rest of the world. As European Central Bank President Jean-Claude Trichet put it on Friday: "We (the euro zone) are the epicenter of this global crisis."

Financial markets are highly anxious about potential defaults by countries like Greece and other heavily indebted European nations and the possibility that Europe's banking system could be at risk given the size of their holdings of debt issued by weak euro zone countries.

"European governments should work alongside the ECB to demonstrate an unequivocal commitment to ensure sovereigns with sound fiscal policies have affordable financing, and to ensure that European banks have recourse to adequate capital and funding to win the full confidence of their depositors and creditors," Geithner said.

The United States has been pushing for a heightened role for the ECB -- the central bank for the 17 nations using the euro as their currency. Washington has pointed to the way that the Treasury and the Federal Reserve cooperated to bolster the financial sector during the 2007-2009 financial crisis.

Geithner and Fed Chairman Ben Bernanke met on Friday with top officials from the European Central Bank and other national central banks from Europe, in part to discuss international financial regulatory reform.

The tempo of warnings to Europe to come together on a solution to its debt issues -- either by avoiding any defaults or by protecting its financial system against the consequences -- has gathered steam but leaders still need time to respond.

"They have six weeks to resolve this crisis," British Finance Minister George Osborne said on Friday, referring to the need to hammer out a definitive plan by the time Group of 20 political leaders meet in Cannes, France, in November.

Geithner said on Saturday indebted countries need time to "demonstrate fiscal discipline" but urged speed in implementing changes to a 440-billion-euro European Financial Stability Facility that were agreed in July and suggested consideration should be given to even more changes.

"Further action to expand the effective capacity of these commitments is still necessary to create a firewall against further contagion," he said, without specifying what action.

G20 participants did not say how the EFSF might be altered and French Finance Minister Francois Baroin used the word "leverage" in comments to reporters on Thursday.

The United States wants Europe to leverage up the EFSF to give it more firepower. One option could be for the ECB to commit large amounts of funding to back up the EFSF.

Germany, as the strongest economy in Europe, plays a central role in any effort to curb a debt crisis.

Finance Minister Wolfgang Schaeuble said on Saturday he will meet his Greek counterpart, Evangelos Venizelos, while in Washington for the IMF meetings.

"We are permanently in contact and talk a lot," Schaeuble said, a day after German Chancellor Angela Merkel sought to dampen speculation about the chances of a Greek default by saying it was not an option for her.

"The damage would be impossible to predict," Merkel warned members of her political party in Germany.

(Additional reporting by IMF reporting team in Washington, Sakari Suoninen in Frankfurt, Writing by Glenn Somerville; Editing by Chizu Nomiyama)