* High crude output, refined product glut drag on prices

* Energy major Shell hit by low prices and profit margins

* Falling China rail freight points to weak economy

(Updates detail, prices, comment; paragraphs 2 and 13)

By Christopher Johnson

LONDON, July 28 (Reuters) - Oil prices steadied just above three-month lows on Thursday as producers continued to pump more than needed, filling inventories, and economic growth prospects darkened.

Brent crude oil was down 10 cents at $43.37 per barrel by 0845 GMT. U.S. light crude was up 5 cents at $41.97.

Both crude benchmarks hit multi-month lows on Wednesday after U.S. government data revealed a surprise rise in crude and gasoline inventories. The build added to an already huge global refined product glut just as slowing economic growth dents the demand outlook.

"U.S. commercial stocks are a good reflection of the oversupplied nature of the global oil market," said Tamas Varga, lead oil analyst at London brokerage PVM Oil Associates.

Oil markets have been dogged by oversupply for the last two years and fell by as much as 70 percent between 2014 and early 2016, when Brent hit the lowest in more than a decade at around $27 per barrel.

Markets have since recovered some ground but oil remains very weak and low refining margins are hurting energy companies.

Energy major Royal Dutch Shell reported a more than 70 percent fall in quarterly profit on Thursday, well below analysts' estimates, as weak oil and gas prices further ate into revenue.

Shell's net income came in at $1 billion in the second quarter, compared with expectations of $2.2 billion and $3.8 billion achieved in the same period last year.

"Lower oil prices continue to be a significant challenge across the business, particularly in the upstream (operations)," said Chief Executive Ben van Beurden.

Mihir Kapadia, CEO at wealth management firm Sun Global Investments, said oil was still being depressed by concerns over a supply glut and waning demand from key international markets.

In China, rail freight volume fell 7.5 percent in the first half of 2016 from the same period a year earlier to 1.58 billion tonnes, the country's top economic planner said on Thursday.

Varga at brokerage PVM said record high stocks and oversupply could drive crude prices down into the mid $30 per barrel area before a significant rally.

"The trend is still down and the bears seem to be in control," Varga said, adding: "But we could see an upside correction before driving lower again."

(Additional reporting by Henning Gloystein in Singapore; Editing by David Holmes and Mark Potter) ((christopher.johnson@thomsonreuters.com; +44 7790 561 651;)(Reuters Messaging: christopher.johnson.reuters.com@reuters.net))