GLOBAL ECONOMY-Euro zone, Japan, U.S. pile on economic gloom

* Euro zone economic sentiment sinks

* Japan's factory output shrinks

* U.S. home mortgages applications fall

* Central banks promise to extend help (Updates with central bank measures)

By Burton Frierson and Marcin Grajewski

NEW YORK/BRUSSELS, July 30 (Reuters) - Japan, Europe and the United States delivered further evidence on Wednesday of economic difficulties while officials pledged to continue efforts to counteract the credit crunch causing the trouble.

Economic sentiment in the euro zone skidded in July to its lowest since March 2003, while Japanese factory output shrank in April-June for the second straight quarter.

Applications for U.S. home loans slowed to their weakest pace since December 2000, the latest sign that the worst housing slump since the Great Depression is still deepening.

President George W. Bush signed into law a rescue package for the housing market, the original source of global financial turmoil, that includes emergency backstops for mortgage financing giants Fannie Mae (FNM.N: Quote, Profile, Research) and Freddie Mac (FRE.N: Quote, Profile, Research).