SINGAPORE, Jan 17 (Reuters) - Oil prices were mixed on Tuesday, supported by Saudi Arabia saying it would adhere to a commitment to cut output, but held back by rising U.S. production and scepticism that OPEC as a whole would comply with its commitments to reduce supplies.

Brent crude futures , the international benchmark for oil prices, were at $55.76 per barrel at 0813 GMT, down 10 cents from their last close.

U.S. West Texas Intermediate (WTI) crude futures , however, were up 15 cents at $52.51 per barrel.

Traders said markets were receiving some support from top crude exporter Saudi Arabia, which said it would adhere strictly to its commitment to cut output under the agreement between OPEC and other producers like Russia.

Under the agreement, OPEC, Russia, and other non-OPEC producers have pledged to cut oil output by nearly 1.8 million barrels per day (bpd), initially for six months, to bring supplies back in line with consumption.

"The market genuinely seems quite happy here (around $55)...but people are watching with caution as the slightest hint of this OPEC/non-OEPC agreement going wrong is going to drive the market down," said Matt Stanley, a fuel broker at Freight Investor Services (FIS) in Dubai.

Despite this, crude futures have fallen 5 percent since their early January peaks.

Because of doubts that over OPEC's and Russia's willingness to fully comply with the cuts, crude futures have fallen around 5 percent since their peaks in early January.

Traders are also eyeing rising U.S. output with interest, as this could offset supply cuts elsewhere.

"The market is focused on the build in U.S. production which is nearly up to 9 million bpd - up from 8.5 million bpd last June and close to 2014 production levels," said Michael McCarthy, chief market strategist at Sydney's CMC Markets.

"With U.S. crude clearly above $50 a barrel, we are getting a supply-side response which is pushing production higher," he said, adding that this "potential oversupply shows this is not the right time to be buying oil."

Further weighing on crude, at least in the short-term, have been refinery outages in the Middle East and Asia over the past week, traders said.

Analysts also said that steps to prop up oil prices through a cut in supplies could be self-defeating.

"For each $10 per barrel increase in oil prices, oil demand will decline by 10 basis points. While consensus expects demand-growth of 1.3 million bpd in 2017 (vs 1.4 million bpd in 2016), we see risks to the downside as demand growth in China and India starts to moderate," AB Bernstein said.

(Reporting by Henning Gloystein; Additional reporting by Keith Wallis; Editing by Joseph Radford and Sonali Paul) ((henning.gloystein@thomsonreuters.com; +65 6870 3263; Reuters Messaging: henning.gloystein.thomsonreuters.com@reuters.net))