UPDATE 3-Oil falls as OPEC, Russia look to raise output amid U.S. surge

* Saudi Arabia, Russia set to raise supplies by 1 million bpd

* U.S. output has surged by more than 27 pct in two years

* But climbing supply from top producers comes amid record demand

* Slumping Venezuela output, Iran sanctions tightened market

* Top oil producers' combined output: https://tmsnrt.rs/2xk67ZR (Updates prices)

SINGAPORE, May 28 (Reuters) - Oil prices fell on Monday, extending even steeper declines from Friday, as Saudi Arabia and Russia said they may increase supplies and as U.S. production gains show no signs of abating.

Brent crude futures were at $75.70 per barrel at 0655 GMT, down 74 cents, or 1 percent, from their last close.

U.S. West Texas Intermediate (WTI) crude futures were at $66.78 a barrel, down $1.1, or 1.6 percent.

Brent and WTI have fallen by 6 percent and 8.3 percent respectively from peaks touched earlier in May.

In China, Shanghai crude oil futures tumbled by 3.8 percent to 462.3 yuan ($72.34) per barrel.

The Organization of the Petroleum Exporting Countries (OPEC), as well as top producer but non-OPEC member Russia, started withholding supplies in 2017 to tighten the market and prop up prices, which in 2016 fell to their lowest in more than a decade at less than $30 per barrel.

But prices have soared since the start of the cuts last year, with Brent breaking through $80 per barrel earlier in May, triggering concerns that high prices would crimp economic growth and stoke inflation.

"The pace of the recent rise in oil prices has sparked a debate among investors on whether this poses downside risks to global growth," Chetan Ahya, chief economist at U.S. bank Morgan Stanley, wrote over the weekend in a note.

To address potential supply shortfalls, Saudi Arabia, de-facto leader of producer cartel OPEC, as well as top producer Russia said on Friday they were discussing raising oil production by some 1 million bpd.

"Crude oil prices collapsed ... after reports emerged that Saudi Arabia and Russia had agreed to increase crude oil production in the second-half of the year to make up for losses elsewhere under the production cut agreement," ANZ bank said on Monday.

Meanwhile, surging U.S. crude production also showed no sign of abating as drillers continue to expand their search for new oil fields to exploit.

U.S. energy companies added 15 rigs looking for new oil in the week ended May 25, bringing the rig-count to 859, the highest level since 2015, in a strong indicator that American crude production will continue to rise.

U.S. crude production has already surged by more than 27 percent in the last two years, to 10.73 million barrels per day (bpd), bringing its output ever closer to Russia's 11 million bpd.

"Oil prices are showing symptoms of a falling knife as investors are jittery on the prospect of increased production from three of the world's top producers," Singapore-based brokerage Phillip Futures said on Monday. ($1 = 6.3909 Chinese yuan renminbi)

(Reporting by Henning Gloystein; Editing by Richard Pullin and Joseph Radford)