* Rising OPEC output, U.S. drilling, weighing on crude markets

* Refined product glut also weighs on oil

* Asia's weakening economies threaten oil demand

(Re-leads with higher prices, adds comment)

By Henning Gloystein

SINGAPORE, Aug 1 (Reuters) - Oil rose on Monday, driven by new orders as traders staked out positions at the start of the new month, but the market remains dogged by plentiful crude supplies, a flood of refined products, and a weakening economic outlook.

Brent crude LCOc1 was at $43.72 per barrel at 0440 GMT, up 19 cents from its last close in July, when it lost 12 percent over the month.

U.S. West Texas intermediate CLc1 was at 41.76 per barrel, up 16 cents from July's last close. WTI shed 13 percent in July.

"Oil prices rose on the day but appear vulnerable to concerns of oversupply," ANZ bank said, with traders pointing to an influx of new orders with the start of August.

Overproduction of crude and a wave of refined products were the main factors weighing on oil.

"Last week's crude build in the U.S. and the return of production in both Canada and Nigeria was a rude awakening that rebalancing (of oil markets) is probably further away than the market thought," Singapore Exchange (SGX) said.

Responding to an expected drop in demand, top exporter Saudi Arabia on Sunday slashed the September price for its light crude for Asian customers by $1.30 a barrel.

This is the largest cut in nearly a year, ahead of an expected fall in demand in October when about 1 million barrels per day (bpd) of refining capacity in Asia will be shut for maintenance. urn:newsml:reuters.com:*:nL8N1AH0GP

Output from the Organization of the Petroleum Exporting Countries (OPEC) in July likely reached its highest in recent history, at 33.41 million bpd from a revised 33.31 million bpd in June. urn:newsml:reuters.com:*:nL8N1AF3LE

In Libya, the state oil company said it welcomed the reopening of oil ports following a deal between the U.N.-backed government and an armed force, saying it would begin work to restart disrupted exports soon. The country is aiming to boost exports to 900,000 bpd by the end of the year. urn:newsml:reuters.com:*:nL8N1AH0LX

In the United States, drillers last week added oil rigs for a fifth consecutive week as part of the biggest monthly rig count increase in over two years, adding three oil rigs to a total of 374. urn:newsml:reuters.com:*:nL1N1AF1LN

Just as oil supplies rise, new economic concerns have emerged.

Japanese manufacturing activity shrank in July and new export orders contracted the fastest in more than 3-1/2 years, a survey showed on Monday. urn:newsml:reuters.com:*:nS7N17W003

In South Korea, July exports fell at the fastest pace in three months, far worse than expectations, contracting 10.2 percent on-year to $41.05 billion. urn:newsml:reuters.com:*:nL4N1AE24T

Its July crude imports fell 5.8 percent from a year earlier to 88 million barrels, official data showed on Monday. urn:newsml:reuters.com:*:nL4N1AF17K

(Reporting by Henning Gloystein; Editing by Michael Perry and Christian Schmollinger) ((henning.gloystein@thomsonreuters.com, +65 6870 3263, Reuters Messaging: henning.gloystein.thomsonreuters.com@reuters.net;))