* OPEC output hit 2018-high in August -survey
* But U.S. sanctions to target Iran's oil exports from November
* U.S. rig count climbs, pointing to more production
* U.S. oil drilling, output & storage: https://tmsnrt.rs/2wc5wpr (Updates throughout, changes dateline, previous SINGAPORE)
LONDON, Sept 3 (Reuters) - Oil prices steadied on Monday, weighed down by rising supply from OPEC and the United States but supported by concerns that falling Iranian output will tighten markets once U.S. sanctions bite from November.
Brent crude oil was up 20 cents at $77.84 a barrel by 0745 GMT. U.S. crude was unchanged at $69.80.
The two benchmarks have risen strongly over the last two weeks with Brent gaining around 10 percent on expectations that global supply will tighten later this year.
"The contracts are in a strong uptrend, but one that looks at the moment to be a bit tired," said Robin Bieber, technical chart analyst at London brokerage PVM Oil Associates.
Output from the Organization of the Petroleum Exporting Countries rose 220,000 barrels per day (bpd) in August to a 2018 high of 32.79 million bpd, a Reuters survey found.
Production was boosted by a recovery in Libyan production and as Iraq's southern exports hit a record.
U.S. drillers added oil rigs for the first time in three weeks, energy services firm Baker Hughes reported on Friday, increasing the rig count by 2 to 862.
The high rig count has helped lift U.S. crude oil production <C-OUT-T-EIA> by more than 30 percent since mid-2016 to 11 million bpd.
But investors are looking ahead to later this year when U.S. sanctions are expected to curb exports from Iran, the third biggest producer in OPEC.
Stephen Innes, head of trading for Asia-Pacific at brokerage OANDA, said Brent was "supported by the notion that U.S. sanctions on Iranian crude oil exports will eventually lead to constricted markets."
Edward Bell, analyst at Emirates NBD bank in Dubai, agreed:
"Iranian production is already showing signs of decline, falling by 150,000 bpd last month ... (as) importers of Iranian barrels will already be moving away from taking shipments."
Meanwhile, trade disputes between the United States and other major economies including China and the European Union are expected to hurt oil demand if they are not settled soon.
China's manufacturing activity grew at the slowest pace in more than a year in August, with export orders shrinking for a fifth month and employers cutting more staff, a private survey showed on Monday.
OANDA's Innes said it was too early to say whether economic slowdown would put a serious dent in oil prices.
"It isn't at all clear that such type of economic headwinds will topple oil prices given ... the constant barrage of supply outages," Innes said.
(Reporting by Henning Gloystein; editing by Jason Neely)