* U.S. drillers cut rig count for first time in 23 weeks
* But rising output from within OPEC weighs on market (Refreshes prices, adds comment)
LONDON, July 3 (Reuters) - Oil pared earlier losses on Monday, resuming its longest stretch of daily rallies in more than five years after data pointed to moderating U.S. output, though analysts said news of rising OPEC production could cap gains.
Brent crude futures were up 26 cents on the day at $49.03 a barrel by 1300 GMT, off a session low of $48.54. The price rose 5.2 percent last week for a first weekly gain in six.
The benchmark Brent price has risen for eight trading days in a row, the longest unbroken stretch of gains since February 2012. U.S. crude futures rose 28 cents to $46.32.
"There may be more upside to come in days ahead, despite sentiment having previously been extremely bearish," said OANDA analyst Craig Erlam.
Speculators in Brent crude futures and options raised their bets against a sustained price rise to the highest level on record in the latest week.
Drilling activity for new oil production in the United States fell for the first time since January, dropping by two rigs, while U.S. government data showed crude output fell in April for the first time this year.
"Sentiment has turned and I think we should be going up (in price). I don't think it's going to last, but the momentum at the moment is with the bulls," PVM Oil Associates strategist Tamas Varga said.
The drop in U.S. rig count and U.S. Energy Information Administration figures showing output fell by 24,000 barrels per day (bpd) on a monthly basis "sent out a short-term bullish message", he said.
The oil price is still down 14 percent this year, with strong global demand not enough to absorb rising output from the United States, Nigeria, Libya and other locations, such as Brazil and the North Sea.
Despite the dip in U.S. drilling, 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.
Oil markets remain oversupplied as output from the Organization of the Petroleum Exporting Countries hit a 2017 high.
"At current output levels OPEC will not succeed in eliminating the inventory overhang completely by year's end," Commerzbank analysts said in a note.
June OPEC production was up by 280,000 bpd at 32.72 million bpd, a Reuters survey showed, despite the group's pledge to hold back output.
"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 AxiTrader, adding that the rise came from Nigeria and Libya, which are exempt from the cuts. (Addtional reporting by Henning Gloystein in Singapore; Editing by Edmund Blair and David Goodman)