* Brent fall below $70/barrel, WTI dips below $65/barrel
* Saudi Arabia proposes long-term supply management with Russia
* Shanghai crude sees high volumes, but also strong volatility
* Shanghai crude drops more than 4 percent to just over 400 yuan/b (Adds crude spreads, chart; updates prices)
SINGAPORE, March 28 (Reuters) - Oil prices fell on Wednesday, with Brent dropping back below $70 per barrel and U.S. West Texas Intermediate crudes dipping below $65, pulled down by a report of increasing U.S. crude inventories that surprised many traders.
U.S. WTI crude futures were at $64.71 a barrel by 0356 GMT, down 54 cents, or 0.8 percent, from their previous settlement.
Brent crude futures were at $69.65 per barrel, down 46 cents, or 0.7 percent.
Traders said the dips came after the American Petroleum Institute (API) late on Tuesday reported a surprise 5.3 million barrels rise in crude sticks in the week to March 23, to 430.6 million barrels.
Official U.S. inventory data will be published by the Energy Information Administration (EIA) late on Wednesday.
"We'll see how the inventory data looks and whether these recent highs can be challenged again. For the moment it is looking like both WTI and Brent are stalling," said Greg McKenna, chief market strategist at futures brokerage AxiTrader.
Wednesday's price falls came despite top exporter Saudi Arabia saying it was working with top producer Russia on a historic long-term pact that could extend controls over world crude supplies by major exporters for many years.
Saudi Crown Prince Mohammed bin Salman told Reuters that Riyadh and Moscow were considering greatly extending a short-term alliance on oil curbs that began in January 2017 after a crash in crude prices.
"We are working to shift from a year-to-year agreement to a 10 to 20 year agreement," the crown prince told Reuters in an interview in New York late on Monday.
AxiTrader's McKenna said such an agreement between Russia and Saudi Arabia "effectively means an expansion" of the Organization of the Petroleum Exporting Countries (OPEC), of which Saudi Arabia is the de-facto leader but in which Russia is not a member.
VOLATILE SHANGHAI CRUDE
In Asia, Shanghai crude oil futures saw their third day of trading continuing with high volume but also volatility.
Spot Shanghai crude futures were down by 4.2 percent on Wednesday, to 408.3 yuan ($65.04) per barrel by 0357 GMT.
In dollar-terms, that puts Chinese crude prices significantly below Brent and only slightly above U.S. WTI.
Since Shanghai crude oil futures were launched on March 26, it would have been profitable to buy the spread between Brent and Shanghai crudes, which has risen from $1.6 per barrel on Monday to $4.6 on Wednesday, while shorting the Shanghai premium over WTI, which has narrowed from $3.1 a barrel on Monday to just 30 cents on Wednesday.
McKenna said he hoped Shanghai crude "gets a lot of traction and we end up with three established global benchmarks", but he cautioned that "the first couple of days have been volatile." ($1 = 6.2774 Chinese yuan renminbi)
(Reporting by Henning Gloystein; editing by Richard Pullin and Aaron Sheldrick)