Both contracts rose despite a strong dollar, which hit a 14-year high. Crude prices often decline when the dollar strengthens, as it then becomes more expensive to hold dollar-denominated oil contracts.
"There are expectations that we'll see supplies start to tighten by the end of the year," said Phil Flynn, analyst at Price Futures Group in Chicago. "We'll get more heating oil demand this weekend and could see a drop in production next week and even last week because of the cold temperatures."
One outlying factor that has flummoxed some analysts has been a series of increases in U.S. inventories at the key oil storage hub in Cushing, Oklahoma. Flynn said this rise has been largely offset by a drop in Gulf Coast inventories.
Crude stocks fell more than expected last week, feeding expectations for another large drop in this week's figures.
Traders said they were starting to square their books ahead of the upcoming Christmas weekend and the week running up to New Year. As a result, and barring major price-moving news, they said markets would likely remain tepid this week.
A deal to cut global supply among OPEC and non-OPEC producers struck this month has boosted oil prices to 17-month highs. The gains have set up 2016 to be the first year since 2012 in which Brent has risen.
"We are in a wait-and-see mood after OPEC-newsflow caused much volatility," said Frank Klumpp, oil analyst at Stuttgart-based Landesbank Baden-Wuerttemberg. "The new balance seems to be between $53 and $57 a barrel on Brent for the next weeks."
Russian energy minister Alexander Novak told Russian newspaper Vedomosti that Russia may extend a production cut beyond the first half of the year if needed.