* Fitch says oil prices above $60 a barrel "may not be sustained"
* Longer-term, IEA says EVs will only modestly impact oil demand (Adds OPEC demand outlook, updates prices)
SINGAPORE, Nov 14 (Reuters) - Oil markets were treading water on Tuesday, continuing the cautious trading seen over the last week as bullish factors such as ongoing OPEC-led production cuts and Middle East tensions are countered by rising U.S. output.
Brent crude futures were at $63.13 per barrel at 0157 GMT, down 3 cents from their last close. U.S. West Texas Intermediate (WTI) crude was at $56.73 per barrel, also down 3 cents.
The dips came after both crude benchmarks early last week hit highs last seen in 2015, but traders said the market had lost some momentum since then.
"Oil is fairly calm. OPEC is talking its book and boosting demand expectations but the U.S. rig count seems to have countered that," said Greg McKenna, chief market strategist at futures brokerage AxiTrader.
Price support came from ongoing output cuts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia, which have contributed to a reduction in excess supplies.
OPEC also raised its oil demand forecast, saying the world would need 33.42 million barrels per day (bpd) of OPEC crude next year, up 360,000 bpd from its previous forecast and marking the fourth consecutive monthly increase in the outlook since July.
OPEC is due to meet on Nov. 30 to discuss further policy, and the group is expected to agree an extension of the cuts beyond their current expiry date in March 2018.
Despite this, traders said they were cautious on betting on further price rises.
"Prices ... are starting to look like a pause or pullback is needed," said McKenna.
U.S. producers have raised output <C-OUT-T-EIA> by more than 14 percent since mid-2016 to a record 9.62 million bpd.
Fitch Ratings said in its 2018 oil outlook that it assumed 2018 "average oil prices will be broadly unchanged year-on-year and that the recent price recovery with Brent exceeding $60 per barrel may not be sustained."
So far in 2017, Brent has averaged at $54.5 per barrel.
Looking further out, the International Energy Agency said on Tuesday global oil demand would only fall modestly due to the expected rise of electric vehicles, with consumption in petrochemicals and other transportation still growing.
In its World Energy Outlook 2018, the IEA estimates there will be 50 million electric vehicles on the road by 2025 and 300 million by 2040, from around 2 million now. This is expected to cut 2.5 million bpd, or about 2 percent, off global oil demand by that time.
Still, the IEA's "New Policies Scenario," based on existing legislation and policy intentions, expects oil prices to rise towards $83 a barrel by the mid-2020s.
(Reporting by Henning Gloystein; Editing by Joseph Radford)