* Prices edge up on bargain-hunting, technical support

* Uncertainty over emerging markets growth, fiber demand prevails

* ICE stocks continue climb to 76,100 bales -ICE data

NEW YORK, Jan 28 (Reuters) - Cotton futures edged higher on Tuesday, buoyed by technically-driven buying and bargain-hunting after the previous session's rout even as investors remained skittish over growth in emerging markets and waning demand.

The most-active March cotton contract on ICE Futures U.S. closed up 0.1 cent, or 0.1 percent, at 84.35 cents a lb.

The contract traded in a tight range of less than 1 cent throughout the day, as uncertainty kept traders on the sidelines.

Stock markets also steadied, pausing from a three-day selloff as investors waited to see what comes out of a U.S. Federal Reserve meeting on Tuesday and Wednesday.

The spot cotton contract started the week with its biggest loss in four months as investor skittishness and chart signals drove long liquidation.

Cotton prices rallied some 5 percent since the start of the year to a near five-month high earlier this month as strong demand for U.S. cotton stoked worries over tight supplies in the world's top exporter.

Even so, global stocks are set to reach a record by end-July, with supplies in top consumer China ballooning due to a government stockpiling policy that is set for overhaul this year.

Uncertainty over how China will unwind the program has kept traders wary of a price rout, and rising worries over the pace of economic growth in emerging markets has further fueled concerns over fiber demand.

"We're seeing consolidation at (technical) support here, around 84 (cents a lb)," said Jack Scoville, vice president with Price Futures Group in Chicago.

"There are still a lot of worries over Chinese demand."

Exchange inventories have been climbing, further adding price pressure as they have eased some concern over tight supplies while the United States finishes ginning its smallest crop in four years.

ICE stocks reached about 76,100 bales on Monday, up from 34,100 bales at the start of the month, according to the most recent ICE data compiled by Reuters.

Effective on Monday, Feb. 3, cotton trading on ICE Futures U.S. will close earlier in the day, shortening trading times.

(Reporting by Chris Prentice; Editing by Chris Reese)