Brent crude futures were at $63.77 per barrel at 0423 GMT, up 16 cents, or 0.25 percent, from their previous close.
U.S. West Texas Intermediate (WTI) crude futures CLc1 were at $60.23 a barrel, up 11 cents, or 0.2 percent.
Despite these increases, Brent and WTI are on course for weekly declines of almost 1 percent and 1.7 percent, respectively.
Traders said that is due to soaring output from the United States, which has risen by 23 percent since the middle of 2016, to 10.37 million barrels per day (bpd).
"The market continues to struggle to shake off an excess supply... (boosted) by increased supply from a growing U.S. shale patch," ANZ Bank said on Friday.
Thanks largely to shale drilling, the United States now produces more crude than top exporter Saudi Arabia. Only Russia pumps more, at almost 11 million bpd.
"It seems only a matter of time before the U.S. becomes the biggest oil producer in the world. The main question which keeps investors busy is when exactly this will be reached," Hans van Cleef, senior energy economist at Dutch bank ABN Amro, said in a note to investors.
Unlike Middle East producers, where output is largely dictated by state-owned oil companies, U.S. producers drill and sell purely based on economics. If prices remain at current levels or rise further, U.S. drillers are profitable and will raise output; if prices stumble, U.S. production will fall.
"The correlation between the U.S. oil production and the oil prices will remain considerable," van Cleef said.
As much as production, oil prices will also depend on demand.
"Global demand will continue to grow by 1.5 million barrels per day in both 2018 and 2019. This would offer enough room for U.S. oil producers to increase production and for OPEC and her allies to minimalise the production cuts towards the end of 2019," van Cleef said.
The Middle East-dominated Organization of the Petroleum Exporting Countries (OPEC) and Russia have been leading an effort since 2017 to withhold production to prop up prices.
(Reporting by Henning Gloystein Editing by Joseph Radford and Christian Schmollinger) ((Henning.firstname.lastname@example.org; +65 6870 3263; Twitter: @hgloystein))