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UPDATE 4-Oil trades near two-month high, but ample supply weighs

* U.S. crude oil inventories seen down for fifth week

* BP CFO says global oil demand looking pretty strong

* OPEC compliance with supply curbs rises, but total output up (Updates prices, adds analyst comment)

LONDON, Aug 1 (Reuters) - Oil traded near $53 a barrel on Tuesday, close to a two-month high, supported by signs that a persistent inventory glut is starting to ease and strong global demand, although stronger OPEC production kept a lid on gains.

U.S. inventory reports due on Tuesday and Wednesday are expected to show crude stocks fell by 2.9 million barrels last week, the fifth straight week of declines. But OPEC production rose in July, a Reuters survey found, despite a deal to cut output.

Brent crude, the international benchmark, was down 9 cents at $52.63 a barrel at 1024 GMT. The contract traded intraday at $52.93, the highest since May 25. U.S. crude was up 1 cent at $50.18.

"The most bullish argument looking forward is that we are now in the second half of the year," said Tamas Varga of oil broker PVM. "Global demand is expected to pick up significantly."

Some forecasters including the International Energy Agency have been raising their demand estimates. Oil company BP, which reported earnings on Tuesday, was upbeat, seeing demand growing by 1.4 to 1.5 million barrels per day (bpd).

"Global demand is looking pretty strong, and prices will firm around the levels seen today," BP Chief Financial Officer Brian Gilvary told Reuters.

The Organization of the Petroleum Exporting Countries, as part of a deal with Russia and other non-members, is reducing output by about 1.2 million bpd from Jan. 1, 2017 until March next year to get rid of excess supply.

OPEC's adherence to its supply cuts has been high but in recent months production has increased due in part to recovering output in countries exempt from the deal.

Oil output by OPEC rose last month by 90,000 bpd to a 2017 high, a Reuters survey found, led by a further recovery in supply from Libya, one of the exempt producers.

The increase means it will take longer for OPEC to clear the excess, analysts at Commerzbank said, although they added such concerns had faded for now.

"At the current OPEC production level, the oil market is likely to show a supply deficit of only around 500,000 barrels per day in the second half of the year," Carsten Fritsch of Commerzbank said.

"In other words, OPEC will not achieve its goal of completely eliminating the oversupply by year's end."

(Additional reporting by Henning Gloystein; Editing by Dale Hudson)