* Weakening Asian manufacturing weighs on crude
* Trump-Kim summit ends early, without agreement
* U.S. crude output hits record 12.1 million bpd -EIA
* But OPEC production cuts squeeze U.S. crude inventories
* U.S. oil output & storage levels: tmsnrt.rs/2VegNR3 (Updates prices)
By Henning Gloystein
SINGAPORE, Feb 28 (Reuters) - Oil prices fell on Thursday amid weakening factory output in China and Japan and record U.S. crude output, although markets remained relatively well supported by supply cuts led by producer club OPEC.
International Brent crude futures were at $66.04 per barrel at 0747 GMT, down 35 cents, or 0.5 percent, from their last close.
U.S. West Texas Intermediate (WTI) crude oil futures were at $56.78 per barrel, down 16 cents, or 0.3 percent, from their last settlement.
Prices were dragged down by surging American crude oil production C-OUT-T-EIA, which has risen by more than 2 million barrels per day (bpd) over the last year, to an unprecedented 12.1 million bpd.
Factory activity in China, the world's biggest oil importer, shrank for a third straight month in February, as export orders fell at the fastest pace since the global financial crisis a decade ago, official data showed on Thursday.
"Further evidence of a slowdown in China hit risk sentiment," said Jasper Lawler, head of research at futures brokerage London Capital Group.
Amid weak demand from China, oil producers are having to cut prices.
Russia's Surgutneftegaz is selling April-loading ESPO crude oil at the lowest level in three months, charging $2.20 to $2.40 per barrel over benchmark Dubai quotes, trade sources said.
In Japan, Asia's second-biggest economy, factory output posted the biggest decline in a year in January as China's slowdown affects the entire region.
Financial markets also came under pressure after a two-day summit between U.S. President Donald Trump and North Korean leader Kim Jong Un in Vietnam's capital Hanoi ended early and without an official agreement.
Still, oil markets remain relatively well supported by supply cuts by the Organization of the Petroleum Exporting Countries (OPEC), which together with some non-affiliated producers like Russia, known as 'OPEC+', agreed late last year to reduce output by 1.2 million bpd to prop up prices.
Because of these cuts, U.S. commercial crude inventories C-STK-T-EIA fell 8.6 million barrels in the week to Feb. 22 to 445.87 million barrels.
"Crude imports into the U.S. fell 1.6 million bpd last week, to a two-decade low," ANZ bank said on Thursday.
Reporting by Henning Gloystein; Editing by Joseph Radford and Richard Pullin