UPDATE 5-Oil set for second weekly fall as rising US supply upsets bulls

* U.S. oil inventories up, but less than expected

* U.S. crude stocks still above five-year average

* Risk of trade war keeps commodities under pressure (Updates prices, adds comment)

LONDON, March 8 (Reuters) - Oil fell on Thursday, following a sharp rise in the dollar, steering prices towards a second consecutive weekly fall against a backdrop of rising U.S. crude production and inventories.

Brent crude futures fell 47 cents to $63.87 per barrel by 1500 GMT. U.S. West Texas Intermediate (WTI) crude futures fell 40 cents to $60.75 a barrel.

Brent was on track for a drop of around 0.7 percent this week, after last week's 4.4 percent slide.

A build-up in U.S. crude inventory reported the previous day was not as large as expected, given that stocks tend to rise towards the end of the winter as refineries conduct maintenance.

But with the threat of the United States sparking a trade war with some of its largest partners, financial markets were on edge. Prices of commodities stayed under pressure.

"Despite the global economy humming, we see fragility in the oil market," said Julius Baer head of commodities and macro research Norbert Ruecker, adding that rising inventories would put pressure on oil prices in the short term.

"Strong shale output growth challenges the market tightening narrative in the medium term," he added.

The dollar rose against the euro, adding further pressure on crude, after the European Central Bank said measures of underlying inflation remained subdued, suggesting a more cautious outlook for the regional economy.

The U.S. Energy Information Administration said on Wednesday that U.S. crude inventories <C-STK-EIA> rose by 2.4 million barrels in the week to March 2 to 425.91 million barrels, less than the 2.7 million barrels analysts had forecast.

China reported a steep monthly drop in crude imports in February, when the Lunar New Year holidays took place. Imports of crude dropped by more than 20 percent to a daily rate of 8.2 million barrels per day (bpd) from 9.4 million bpd in January.

Reuters commodities columnist Clyde Russell said imports in January and February combined gave a daily rate of 9.02 million bpd, up 10.8 percent from the same period last year.

Rising U.S. output, which reached 10.37 million bpd last week, remains a focus for investors.

"Crude is ... under pressure from rising U.S. production, which hit a new high last week, now firmly above Saudi Arabia's production level," said William O'Loughlin, investment analyst at Australia's Rivkin Securities.

U.S. output is expected to surge beyond 11 million bpd by late 2018, surpassing current No. 1 producer Russia.

This U.S. increase is putting pressure on the Organization of the Petroleum Exporting Countries, Russia and other nations that have curbed output to prop up prices but risk losing market share.

(Additional reporting by Henning Gloystein and Roslan Khasawneh in SINGAPORE Editing by Edmund Blair)