* EIA raises its U.S. shale oil output from last record
* U.S. April shale output to be 6.95 mln bpd -EIA
* March shale output of 6.82 mln bpd already a record
* Shale has driven overall U.S. output to over 10 mln bpd
* U.S. crude output to break through 11 mln bpd this year -IEA
By Henning Gloystein
SINGAPORE, March 13 (Reuters) - Oil prices fell on Tuesday, extending falls from the previous day, as the relentless rise in U.S. crude output weighed on markets.
U.S. West Texas Intermediate (WTI) crude futures were at $61.20 a barrel at 0122 GMT, down 16 cents, or 0.2 percent, from their previous close.
Brent crude futures were at $64.80 per barrel, down 15 cents, or 0.2 percent.
Both crude benchmarks dropped by around 1 percent the previous session.
"Oil prices fell on the back of concerns that surging U.S. production ... could push inventories in the U.S. higher," ANZ bank said on Tuesday.
U.S. crude oil production C-OUT-T-EIA soared past 10 million barrels per day (bpd) in late 2017, overtaking output by top exporter Saudi Arabia.
U.S. production is expected to rise above 11 million bpd by late 2018, taking the top spot from Russia, according to the International Energy Agency (IEA).
The rising U.S. output comes largely on the back of onshore shale oil production.
U.S. crude production from major shale formations is expected to rise by 131,000 bpd in April from the previous month to a record high 6.95 million bpd, the U.S. Energy Information Administration (EIA) said in a monthly productivity report on Monday.
That expected increase would top the 105,000 bpd climb in March from the previous month, to what was then expected to be a record high of 6.82 million bpd, the EIA said.
The EIA is due to publish its latest weekly U.S. production data on Wednesday.
Reporting by Henning Gloystein Editing by Joseph Radford