Brent crude oil futures were at $71.67 a barrel at 1044 GMT, up 84 cents and heading for a weekly gain of 1.9 percent, their third weekly gain in a row.

US West Texas Intermediate (WTI) crude futures were at $64.53, up 95 cents and set for a weekly rise of 2.3 percent, their sixth straight week of gains.

"For the momentum to continue next week, WTI needs to close today above $64 a barrel and preferably break the resistance of $65 a barrel. Volume has been very strong throughout the week," said Petromatrix's Olivier Jakob.

Oil markets have been lifted by more than a third this year by supply cuts led by the Organization of the Petroleum Exporting Countries (OPEC), US sanctions on oil exporters Iran and Venezuela, plus escalating conflict in Libya.

The head of Libya's National Oil Corporation warned on Friday that renewed fighting could wipe out crude production in the country.

"We see Brent and WTI prices averaging $75 per barrel and $67 per barrel respectively through the rest of this year, but risk is asymmetrically skewed to the upside," RBC Capital Markets said in a note.

"Geopolitically infused rallies could shoot prices toward or even past the $80 per barrel mark for intermittent periods this summer."

OPEC and its allies meet in June to decide whether to continue withholding supply. Though OPEC's de-facto leader, Saudi Arabia, is considered keen to keep cutting, sources within the group said it could raise output from July if disruptions continue elsewhere continue.

On the demand side, most of the world's growth in fuel consumption is coming from Asia, where China's economic growth is expected to slow to its lowest in nearly 30 years at 6.2 percent this year, a Reuters poll showed on Friday.

However, concern over such a slowdown was muted on Friday.

"While macro fears of an economic hard landing may be overblown, the concentration risk of global oil demand (in Asia) remains underappreciated," RBC Capital Markets said.