* Cotton swings between 100- and 200-day MA

* Investors book profits after Fed-inspired rally

* Data shows over 100,000 running bales sold in week to Sept. 12

NEW YORK, Sept 19 (Reuters) - Cotton futures fell over 1 percent and erased the previous day's gains on Thursday on technical selling after prices touched a one-month high and tested a long-term resistance.

The market initially extended Wednesday's gains breaking out of its recent range and hitting 85.78 cents per lb, its highest level since Aug. 21, following the Federal Reserve's surprise decision to continue its bond buying program for now.

The market erased those gains as technical selling was triggered after prices touched a 100-day moving average at 85.90 cents.

The most-active December cotton contract on ICE Futures U.S. finished down 0.82 cents, or 0.95 percent, to settle at 85.54 cents a lb. The market found support at its 200-day moving average at 84.28 cents per lb.

"Despite today's retrenchment, we believe the chart looks constructive and will better today's high in the coming days," said INTL FCStone analyst Andy Ryan.

Futures and physical activity was low due to holidays in China, the world's largest textile market.

The market also digested data that showed tapering demand from foreign mills as prices rallied last week.

Some 103,100 running bales of cotton were sold for export in the week to Sept. 12, the U.S. government data showed, down from 134,400 bales in the previous week.

China bought the lion's share - 57,000 bales - followed by Turkey and Peru.

In broader markets, the U.S. dollar recovered from steep losses on Wednesday following the Fed's shock decision to keep its stimulus program intact.

The Thomson Reuters-Jefferies CRB index made up of 19 commodities closed up 0.34 percent. (Reporting by Josephine Mason; editing by Andrew Hay)