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Nov 20 (Reuters) - Industrial demand for silver should rise in both 2013 and 2014, due to improving outlooks for the auto industry and the manufacturing sector, after it declined this year, GFMS, a metals research firm and Thomson Reuters unit, said on Tuesday.

Silver's use in industrial applications is expected to gain nearly 7 percent to 484 million ounces in 2013 and an additional 6 percent to a record 511.6 million ounces in 2014, GFMS said in a report Thursday for the Silver Institute, a trade group.

The report suggests that the price of silver has room to climb in the next several years because of its use in industrial applications, the biggest component in silver fabrication demand.

Total silver fabrication demand includes industrial applications, jewelry, photography, coins and metals, and silverware.

Last week, the global head of metals analytics at GFMS told Reuters that silver prices may climb as much as 38 percent in 2013 from current levels.

Year to date, silver is up 20 percent, doubling gold's gain and is among the best-performers among all commodities.

On Tuesday, silver edged down to around $33 an ounce. In April 2011, it surged to a record near $50 an ounce only to lose about a third of its value in the following week, triggering heavy losses in many other commodities in the so-called "commodities flash crash."

For 2012, GFMS forecast silver industrial demand to be down 6 percent to 454.4 million ounces, citing a sluggish global economy particularly due to challenges posed by a three-year-old European debt crisis.