UPDATE 1-US's Geithner warns Europe crisis a global threat

* Europe's crisis a threat to rest of world

* Geithner says Europe moving too slowly

* Preparing for new push at G20 talks next week

(Recasts lead, adds quotes, background, comments on Wall Street protesters)

WASHINGTON, Oct 5 (Reuters) - Europe needs to step up efforts to control its debt crisis before it pulls the United States and the rest of world into a renewed downturn, Treasury Secretary Timothy Geithner urged on Wednesday.

Speaking at the Washington Ideas Forum in the downtown Newseum, Geithner mixed praise and criticism of Europe as he continued an ongoing effort to push its policymakers toward a more forceful approach toward dealing with debt woes.

"Europe matters a lot to us. We don't want to see Europe weakened by a protracted crisis. Europe understands that," he said but left no doubt at his impatience with progress so far.

"They are moving too slowly," Geithner said. "Europe is a large part of the global economy, and a severe crisis in Europe would be damaging" around the world.

He sidestepped a question about how close the U.S. economy might be sliding back into recession, however.

Asked whether he agreed with Federal Reserve Chairman Ben Bernanke that U.S. growth was close to faltering, Geithner said that growth is "slower, weaker" in the United States and around the world than hoped at the start of the year.

Geithner has met European counterparts in France and in Poland in recent weeks to push for stronger action, including possible leveraging of an established European bailout fund, to a debt crisis now raging in countries like Greece from spreading to Bigger European economies.

He travels to Paris next week to again meet group of 20 finance ministers Oct 14-15 and is expected to pick up the refrain that they must move faster and more convincingly to persuade financial markets that governments are determined to stop the crisis.

Geithner said he believed Europe has decided it will "escalate substantially" its response, and he is confident that they will do so.

"They have the financial resources as a continent that are very large relative to this crisis. It is just a matter of moving more quickly and more forcefully," he said.

"I expect they will do that."

Geithner avoided a direct response when asked whether he supported the "Occupy Wall Street" protesters who have staged continuing demonstrations against what they see as excessive pay for bankers amid high rates of joblessness for young Americans. He said he was sympathetic toward people who feel they have lost a sense of future opportunities that use to be plentiful in America.

Geithner was on the front lines dealing with the 2007-2009 financial crisis that drove the United States into recession -- first as president of the New York Federal Reserve Bank and later as the Obama administration's Treasury chief.

He said the key lesson to be taken from battling crises is that it is necessary to move strongly to quell them and then to not let up before the problems are dealt with and growth can resume.

"The basic problem and reason why governments make these things harder over time is that what happens is the political costs of the initial response is so difficult, so devastating as you saw in the United States, that people tend to pull back too early and leave the job unfinished," Geithner said.

(Reporting by Stella Dawson and Glenn Somerville, editing by Diane Craft)