* U.S. drillers cut rig count for first time in 23 weeks
* But rising output from within OPEC weighs on market (Adds comment, updates prices)
SINGAPORE, July 3 (Reuters) - Oil prices rose on Monday, lifted by the first fall in U.S. drilling activity in months, although gains were capped by reports of rising OPEC output last month even as the group has pledged to cut supply.
Brent crude futures climbed 16 cents, or 0.3 percent, to $48.93 per barrel by 0248 GMT, after jumping 5.2 percent last week, its first weekly gain in six weeks.
U.S. West Texas Intermediate (WTI) crude futures rose 24 cents, or 0.5 percent, to $46.28 per barrel, adding to last week's 7 percent gain.
Prices were lifted as drilling activity in the United States for new oil production fell for the first time since January, dropping by two rigs.
Australian futures brokerage AxiTrader said on Monday in a note that this was "the first crack in the resolve of U.S. shale oil to continue to ramp up production regardless of the big fall in price" earlier this year.
U.S. crude futures fell 9 percent during the second quarter that ended in June while Brent futures declined 9.3 percent. That extended first-quarter losses for the contracts.
Despite the dip in U.S. drilling activity, 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 .
Also, global oil markets remain oversupplied as output from within the Organization of the Petroleum Exporting Countries (OPEC) hit a 2017 high.
June OPEC production was up by 280,000 barrels per day (bpd) to 32.72 million bpd, according to a Reuters survey, despite the group's pledge to hold back output in an effort to tighten the market.
"To put that in context, that is nearly a quarter of the 1.2 million barrels (per day) OPEC agreed to cut," said Greg McKenna, chief market strategist at Australian futures brokerage AxiTrader, adding this increase was driven by higher output from Nigeria and Libya, who were exempted from the cuts. (Reporting by Henning Gloystein; Editing by Richard Pullin and Christian Schmollinger)