Brent crude settled up 41 cents, or 0.7 percent, at $62.86 a barrel while U.S. West Texas Intermediate crude ended 15 cents, or 0.3 percent, higher at $57.62 a barrel.
"Demand remains firm which is the main reason for us to still see oil at above $60 per barrel," said Georgi Slavov, head of research at Marex Spectron.
Faster-than-expected growth in demand this year has given tailwind to OPEC's efforts to clear the glut and the latest U.S. inventory reports are likely to show a third straight weekly drop in crude stocks.
Analysts expect data from industry group American Petroleum Institute (API) and the government's Energy Information Administration (EIA) to show crude stocks fell 3.4 million barrels last week.
The API report is out at 4:30 p.m. EST (2130 GMT), followed by government data on Wednesday at 10:30 a.m. EST.
"We've got upcoming inventory reports today and tomorrow which could assist in giving the market more information to work off," said Tony Headrick, energy market analyst at CHS Hedging LLC.
Analysts looking to next year believe some tightening in supply will continue. Morgan Stanley analysts said in a note on Monday they expect demand to outpace supply in 2018, with most of the supply growth coming from the United States and Canada.
Goldman Sachs late Monday raised its forecast for 2018 Brent and WTI to $62 and $57.50 a barrel, respectively, thanks to OPEC's resolve in maintaining production cuts.
The Organization of the Petroleum Exporting Countries, Russia and other non-OPEC producers last week extended the deal to cut output by 1.8 million barrels per day (bpd) until the end of 2018 to get rid of excess oil in storage.
OPEC has shown strong compliance with the supply cut pledge and in November output fell by 300,000 bpd to its lowest since May, according to a Reuters survey.
"Yesterday was defined by profit taking in post-OPEC trade," he said, adding that the market is now watching for further signals on what 2018 will look like.
The OPEC-led producer group's Nov. 30 decision to extend their supply-cutting deal could bolster U.S. shale drilling given overall higher prices.
Data last week showed U.S. crude output rose to nearly 9.5 million bpd in September, approaching the high of 9.63 million bpd seen in 2015.
(Additional Reporting by Alex Lawler and Jane Chung; Editing by Susan Fenton and Marguerita Choy)
By David Gaffen