By Devika Krishna Kumar

NEW YORK (Reuters) - Oil prices edged higher on Tuesday, with U.S. crude touching its highest since December 2014, supported by OPEC-led production cuts and expectations that U.S. crude inventories have dropped for an eighth week in a row.

The Organization of the Petroleum Exporting Countries and allies including Russia are keeping supply limits in place in 2018, a second year of restraint, to reduce a price-denting glut of oil held in inventories.

U.S. West Texas Intermediate (WTI) crude <CLc1> rose $1.23, or 2 percent, to settle at $62.96 a barrel after touching its highest since December 2014 at $63.24.

Brent crude <LCOc1> ended the session up $1.04, or 1.5 percent, at $68.82 per barrel after hitting a session high of $69.08, its highest since May 2015. Both contracts had their strongest close since December 2014.

Prices extended gains in post-settlement trade after industry group the American Petroleum Institute said crude inventories fell by 11.2 million barrels in the week to Jan. 5 to 416.6 million, compared with analysts' expectations for a decrease of 3.9 million barrels. [API/S]

If confirmed by U.S. government data at 10:30 a.m. EST (1530 GMT) on Wednesday, the draw will be the largest since Sept. 2, 2016. U.S. stockpiles fell by 14.5 million barrels during that week.

"You're so long this market at this point, you could certainly get more interest at these levels," said Rob Haworth, senior investment strategist at U.S. Bank Wealth Management.

"This is a little more confirmation of what speculators have been looking for and after tomorrow's (U.S. government inventory) report, we'll see if they look to do some profit-taking."

OPEC is cutting output by even more than it promised and the restraint is reducing oil stocks globally, a trend most visible in the United States, the world's largest and most transparent oil market. [OPEC/O]

"We expect oil demand growth to outpace non-OPEC supply growth in both 2018 and 2019," Standard Chartered analysts said in a note.

"In our view, the back of the Brent and WTI curves are both still underpriced. We do not think that prices below $65 per barrel are sustainable into the medium term."

Many producers, still suffering from a 2014 price collapse, are enjoying the rally, although they are wary it will spur rival supply sources. Iran said OPEC members were not keen on increased prices.

The rise in prices is expected to drive gains in U.S. production during 2018, offsetting curbs by others.