* Brent has risen by more than 10 pct since December
* Oil supported by OPEC-led cuts, strong economic growth
* Tensions in OPEC member Iran have also lifted prices
* Soaring U.S. crude production could undermine rally (Updates prices, adds OPEC)
SINGAPORE/LONDON, Jan 8 (Reuters) - Oil prices rose on Monday, coming close to new three-year highs on a slight decline in the number of U.S. rigs drilling for new production and sustained OPEC output cuts.
U.S. West Texas Intermediate (WTI) crude futures had risen to $61.94 a barrel by 1140 GMT, 50 cents above their last settlement. WTI last week reached $62.21, the highest since May 2015.
Brent crude futures were at $67.95 a barrel, 33 cents above their last close. Brent hit $68.27 last week, the highest since May 2015.
Traders said the gains were due to a slight decline in the number of U.S. rigs drilling for new production. The rig count eased by five in the week to Jan. 5 to 742, according to data from oil services firm Baker Hughes.
Despite this, U.S. production <C-OUT-T-EIA> is expected soon to rise above 10 million barrels per day, largely thanks to soaring output from shale drillers. Only Russia and Saudi Arabia produce more.
"The U.S. oil price is now into a range that is anticipated to attract increased shale oil production," said Ric Spooner, chief market analyst at CMC Markets in Sydney.
"Traders may decide that discretion is the better part of valor while markets wait on evidence of what happens to the rig count and production levels over the next couple of months."
Rising U.S. production is the main factor countering output cuts led by the Middle East-dominated Organization of the Petroleum Exporting Countries and by Russia, which began in January last year and are set to last through 2018.
A senior OPEC source from a major Middle Eastern oil producer said on Monday that OPEC was monitoring unrest in Iran as well as Venezuela's economic crisis, but will boost output only if there are significant and sustained production disruptions from those countries.
Stephen Innes, head of trading for Asia/Pacific at futures brokerage Oanda in Singapore, said "the OPEC vs shale debate will rage" this year, being a key price-driving factor.
However, Innes added that Middle East turmoil would remain a key focus for oil markets and had the potential to "send oil prices rocketing higher." (Reporting by Henning Gloystein, Florence Tan and Dmitry Zhdannikov; Editing by Dale Hudson)