* U.S. drillers cut rig count for first time in 23 weeks
* But rising output from within OPEC weighs on market
By Henning Gloystein
SINGAPORE, July 3 (Reuters) - Oil prices edged up on Monday, supported by the first fall in U.S. drilling activity in months, although rising output from OPEC despite a pledge to cut supplies capped gains.
Brent crude futures added 6 cents or 0.1 percent to $48.83 per barrel by 0137 GMT, after jumping 5 percent last week for the first gain in six weeks.
U.S. West Texas Intermediate (WTI) crude futures rose 15 cents, or 0.3 percent, to $46.19 per barrel after a more than 7 percent gain last week from depressed levels.
Traders said U.S. prices were relatively stronger than Brent after U.S. drilling activity fell for the first time since January. Sentiment for the global Brent benchmark was more subdued due to rising output from within the the Organization of the Petroleum Exporting Countries (OPEC).
"For the first time in 23 weeks, the number of drill rigs operating in the U.S. fell, down 2 to 756," ANZ bank said on Monday, but added that "this exuberance may be tempered by news over the weekend that Libya oil production hit another record."
Despite the drop, the total rig count was still more than double the 341 rigs in the same week a year ago, according to energy services firm Baker Hughes Inc.
The slight cut in U.S. drilling for new production was met by a rise in output from within OPEC in June, up by 280,000 barrels per day (bpd) to an estimated 2017 high of 32.72 million bpd despite the group's pledge to hold back production in an effort to tighten the market.
OPEC's high output is largely down to rising production from members Nigeria and Libya, which were exempted from the output cuts, and whose surge in supplies has undermined efforts by other members like Saudi Arabia to restrict supplies.
Reporting by Henning Gloystein; Editing by Richard Pullin