Oil was steady above $68 on Thursday, after settling unchanged a day earlier, as a steep fall in U.S. gasoline inventories offset a smaller-than-expected drop in crude stocks in the world's top energy user.

Traders will scour weekly jobless claims and a gauge of non-manufacturing sector activity for August due later for clues on how strongly the U.S. economy is recovering.

By 0215 GMT, U.S. crude for October delivery was up 3 cents at $68.08 a barrel. London Brent crude fell 18 cents to $67.48 a barrel.

While steady for the last two days, oil is still down over 6 percent so far this week, dropping nearly $5 a barrel on Monday and Tuesday as worries over the health of the global economy and the U.S. financial sector sent investors scurrying for cover.

The main drivers will be the U.S. dollar and the stock market, which is currently in a correction phase, so the crude market is going through the same, said Sumisho Sano, General Manager of SCM Securities Research.

The stock market has largely discounted the recovery of the economy. Sentiment will be weak in the short term.

U.S. inventories sent mixed signals, with a 400,000 barrel drop in crude stocks last week, but gasoline inventories showing a steep 3 million barrel drop as U.S. fuel demand rose slightly over year-earlier levels.

Economic data was also not convincing, with U.S. private employers cutting 298,000 jobs in August, less than July but more than the 250,000 job losses economists had expected, while new orders at U.S. factories rose by 1.3 percent in July, but below economists' expectations.

Key economic data due later is expected to provide more trading cues.

At 1230 GMT, the U.S. Labor Department will release first-time claims for jobless benefits for the week ended Aug 29. Economists polled by Reuters forecast a total of 560,000 new filings, down from 570,000 in the prior week.

The Institute for Supply Management (ISM) will unveil its August non-manufacturing index at 1400 GMT. Economists forecast a higher reading of 48.0 versus 46.4 in July.

Traders were also eyeing news that big oil producers are increasing output. Russian oil output hit a record high in August, nearing 10 million barrels per day as the country launched a new giant field.

Supply from the Organization of the Petroleum Exporting Countries rose in August for a fourth consecutive month, taking overall output discipline to 68 percent of the target from a revised 70 percent in July, a Reuters survey showed.

OPEC is likely to keep output targets steady when it meets September 9, a Kuwaiti OPEC delegate said.

(Editing by Michael Urquhart)

OPEC