NEW YORK, Jan 15 (Reuters) - The number of rigs drilling for natural gas in the United States jumped 30 this week to a 10-month high of 811, according to a report on Friday by oil services firm Baker Hughes in Houston.

The U.S. natural gas drilling rig count has rebounded sharply after bottoming at 665 on July 17, its lowest level since May 3, 2002, when there were 640 gas rigs operating.

But the rig count is still well off its recent peak above 1,600 in September 2008, standing at 424 rigs, or 34 percent, below the same week last year.

Many gas producers had scaled back drilling operations earlier this year with credit tight and natural gas cash prices sinking this summer to $2.50 per million British thermal units (mmBtu), a 7-1/2 year low and down some 80 percent from July 2008 highs above $13.

But cash gas prices have rebounded nearly 150 percent since hitting their summer lows, averaging more than $6 so far this month, a level high enough to encourage more onshore drilling, particularly in some of the prolific shale basins.

While drilling is still down over the past year or so, traders noted production has not slowed that much, with recent government data estimating that January marketed gas output will be about 2.3 percent lower than in January 2009.

Many traders agreed rig cuts may be necessary to balance the market, with gas inventories still at fairly high levels for this time of year and demand, particularly from the industrial sector, down sharply due to the recession. (Reporting by Joe Silha; Editing by John Picinich)