* Crude oil rises this week after five weeks of decline
* OPEC has been pushing to curb output, fight glut
* U.S. output still growing, rig count highest in over 3 yrs (Adds comment, updated prices)
By Naveen Thukral
SINGAPORE, June 27 (Reuters) - Oil prices rose for a fourth consecutive session on Tuesday as investors covered short positions, although worries over a persistent global supply glut still lingered.
Brent crude futures, the international benchmark for oil prices, gained 35 cents, or 0.7 percent, to $46.18 per barrel by 0715 GMT.
U.S. West Texas Intermediate (WTI) crude futures were up 30 cents, or 0.7 percent, at $43.68 per barrel.
The gains mean the market is up slightly so far this week, after spending much of the last month in negative territory.
"Oil may be close to the bottom but badly damaged sentiment and a rising (U.S.) rig count will dent the recovery," U.S. bank Citi said on Tuesday.
The Organization of the Petroleum Exporting Countries (OPEC) and its partners have been trying to reduce a global crude glut with production cuts. OPEC nations and 11 other exporters agreed in May to extend cuts of 1.8 million barrels per day (bpd) until March 2018.
Despite the cuts, which started in January, markets remain well supplied due to rising output elsewhere.
OPEC members Nigeria and Libya are exempt from the cuts and have raised production. OPEC member Iran was also allowed a small increase to recover market share lost under Western sanctions over its nuclear programme.
U.S. shale oil output has risen about 10 percent since last year to 9.4 million bpd C-OUT-T-EIA, with the number of U.S. oil rigs in operation at the highest in more than three years.
"Traders are also looking ahead to the EIA Energy Conference in Washington, where U.S. shale oil producers are expected to give their view of current market conditions," ANZ bank said.
Analysts at Bank of America-Merrill Lynch said demand was not growing quickly enough to absorb output, especially since imports in Asia are stuttering.
A fuel glut in China, a hangover from demonetisation in India, and an ageing, declining population in Japan are holding back crude oil demand growth in three of the world's top four oil buyers. (Reporting by Naveen Thukral; Editing by Joseph Radford and Tom Hogue)