* U.S. crude output hits record 10.9 mln bpd
* OPEC, Russia also expected gradually to increase production
* Fractured opinions within OPEC (Updates prices)
LONDON, June 14 (Reuters) - Oil prices mostly steadied on Thursday, but were likely to remain under pressure from evidence of rising U.S. output and uncertainty over the outlook for supply before a meeting next week of the world's largest exporters.
Brent crude futures were down 7 cents at $76.67 a barrel by 1107 GMT, while U.S. West Texas Intermediate (WTI) crude futures were up 27 cents at $66.91.
"At OPECs meeting in a good weeks time, Saudi Arabia apparently plans to make several proposals that all boil down to increasing production on a one-off or gradual basis by between 500,000 and 1 million barrels per day," Commerzbank analysts said in a note.
"Iran has already signaled that it will resist any such attempts and blames the U.S. for the price rise. According to sources close to OPEC, Venezuela and Iraq are also not in favor of raising production."
The Organization of the Petroleum Exporting Countries meets on June 22 in Vienna to discuss its own supply policy and then again on June 23 with rival producers such as Russia and Oman.
For the last month, oil prices have successively marked lower intraday highs and lows, indicating that traders and investors are not quite as confident in the outlook for the supply/demand balance, especially given the steep rise in U.S. crude production and the splintering within OPEC.
U.S. crude output has risen almost 30 percent in the last two years to 10.9 million bpd. It is now close to that of top global producer Russia, which churned out 11.1 million bpd in the first two weeks of June, and above top exporter Saudi Arabia, which produced slightly more than 10 million bpd.
But the rising output was met by strong demand, which traders said prevented prices from falling further.
U.S. consumption of gasoline rose to a record 9.88 million bpd last week, according to government figures.
U.S. crude inventories <C-STK-T-EIA> fell by 4.1 million barrels, to 432.4 million barrels.
WORLD CUP MEET
The surge in U.S. output puts pressure on other producers, which are losing market share.
Russian and Saudi production has been held back voluntarily since 2017, when OPEC, together with a number of non-OPEC producers, started supply cuts of 1.8 million bpd to prop up prices.
With Brent prices up by around 180 percent from their 2016 lows and demand strong, OPEC and Russia may soon end their supply cuts.
OPEC's effective leader Saudi Arabia and Russia will also have the chance to talk before the Vienna meeting.
Russia and Saudi Arabia are set to open the football World Cup tournament, which starts in Russia on Thursday.
"The topic will surely come up between President (Vladimir) Putin and the Saudi Crown Prince Mohammad bin Salman as they watch their countries teams in todays opening game of the football World Cup together in Moscows Luzhniki stadium," PVM Oil Associates strategist Tamas Varga said.
(Reporting by Amanda Cooper; Editing by Adrian Croft and Dale Hudson)