Brent crude was down 74 cents, or 1.1%, at $67.26 a barrel by 0745 GMT after dropping 0.6% on Wednesday.
U.S. oil was also down 65 cents, or 1%, at $63.95 a barrel, having fallen 0.3% the previous session.
Both contracts are down around 3% over the last five days of declines.
Data on Wednesday showed U.S. crude inventories have risen for four straight weeks after refineries in the south were forced to shut due to severe cold weather.
Stocks of gasoline and diesel increased against expectations among analysts for a decline.
On the demand front, a slowdown in some inoculation programmes and the prospect of more restrictions to control the coronavirus tempered expectations for a recovery in fuel use, Reuters said.