* Iraq sees some flexibility for OPEC, non-OPEC deal
* Kuwait reiterates OPEC cannot cut oil output alone
* China rail freight decline adds to economic concerns
* U.S. crude stocks seen up; API report due at 2130 GMT (Updates prices)
By Alex Lawler
LONDON, Jan 26 (Reuters) - Oil rose further above $30 a barrel on Tuesday, lifted by hopes that OPEC and non-OPEC producers may be edging closer to a deal to tackle one of the biggest supply gluts in decades.
The Organization of the Petroleum Exporting Countries is making renewed calls for rival producers to cut supply alongside its members, but Russia, seen as key to any deal, has so far refused to cooperate. Oil Minister Adel Abdel Mahdi said on Tuesday he saw "some flexibility" for a deal. Such an idea has been repeatedly mooted and dismissed for over a year.
Brent crude LCOc1 was up 37 cents at $30.87 a barrel by 1400 GMT, rebounding from an earlier decline. It reached $27.10, its lowest since November 2003, on Jan. 20. U.S. crude CLc1 was up 32 cents at $30.66.
"Without a production agreement, fundamentals point to lower numbers," said David Hufton of oil brokers PVM. "With one, oil becomes a $40-to-$60-a-barrel market."
Demand concerns limited the rally. China's annual rail freight volume fell 11.9 percent in 2015 versus a drop of 3.9 percent in 2014, adding to worries about contracting economic activity in the second-largest oil consumer. of a sharp slowdown in economic growth, particularly in China, are dragging down global stock markets from arguably overheated levels," analysts at Energy Aspects said in a report. "This is weighing on other risky assets, including oil."
Despite a price collapse and spending cutbacks across much of the industry, major OPEC producers are sticking to investment plans and some intend to boost supply.
The risk of prices staying low for a longer time is not deterring Kuwait from investing in energy projects, the head of Kuwait Petroleum Corp said on Tuesday, echoing similar comments from the chairman of Saudi Arabia's state oil company.
Iraq may further boost output this year, a senior Iraqi oil official, who asked not to be identified, said on Monday. Production hit a record in December. are now watching the U.S. Federal Reserve policy meeting starting later in the day, the first since the central bank raised interest rates in December, for clues on the movement of the dollar. the glut, analysts expect the latest weekly reports on U.S. supplies to show crude inventories, already close to a record high, rose further. EIA/S
The American Petroleum Institute, an industry group, releases its supply report at 2130 GMT and the government's data is due on Wednesday.
(Additonal reporting by Meeyoung Cho in Seoul; editing by Jason Neely and David Evans)