* Crude fell previous day after China warning spooked markets
* But overall oil supply/demand fundamentals are tightening
* Global refiners import U.S. oil to make up for OPEC cuts (Adds comment, backwardation; updates prices)
SINGAPORE, Oct 20 (Reuters) - Oil prices edged up on Friday, supported by signs of tightening supply and demand fundamentals, although a warning about excessive China economic optimism still weighed somewhat on markets.
Brent crude futures, the international benchmark for oil prices, were at $57.39 at 0420 GMT, up 16 cents, or 0.28 percent from their last close.
U.S. West Texas Intermediate (WTI) crude futures were at $51.47 per barrel, up 18 cents, or 0.35 percent.
The stable prices came after a more than 1 percent fall in prices the previous day.
This was put down to profit-taking following four days of straight gains, but also to a sudden market slump which spooked traders after the veteran but outgoing governor of China's central bank warned of a "Minsky moment", a reference to excessive optimism about economic growth fuelled by vast debt and speculative investment.
Much of that concern had dissipated by Friday, however, and analysts said there were indicators of a tightening oil supply and demand fundamentals.
"Oil market has moved into modest under-supply and we expect this will persist at least through the end of the year," U.S. investment bank Jefferies said.
U.S. commercial crude oil stocks have dropped 15 percent from their March records, to 456.5 million barrels, below levels seen last year. <C-STK-T-EIA>
Part of this drawdown has been due to rising exports as a result of the steep discount of WTI crude to Brent, which makes it attractive for American producers to export their oil. <CL-LCO1=R>
Additionally, crude futures price curves are in backwardation, which makes it attractive to sell produced oil immediately rather than store it for later dispatch.
RBC Capital Markets said, "a strong indicator that global inventories are being run down will be when the market starts relying on U.S. exports to fill deficits."
That moment may have arrived.
Shipping data in Thomson Reuters Eikon shows that overseas U.S. crude oil shipments have soared from virtually zero before the government loosened export restrictions in late 2015 to around 2.6 million barrels per day (bpd) in October.
"Physical bottlenecks are unlikely to kick in until waterborne (U.S.) exports approach 3.2 million bpd," RBC Capital Markets said.
Exports have been boosted since a production cut led by the Organization of the Petroleum Exporting Countries (OPEC) has been in place since January this year, and which OPEC wants to expend beyond its current expiry date at the end of March 2018.
"Our expectation is that OPEC (and partners including Russia) will extend production cuts through the end of 2018," Jefferies bank said.
(Reporting by Henning Gloystein; Editing by Kenneth Maxwell)