By Sonali Paul

MELBOURNE/BEIJING (Reuters) - Oil prices edged up on Friday, heading for their biggest weekly gains since mid-December, fuelled by supply worries amid escalating unrest in Kazakhstan and outages in Libya.

Brent crude futures climbed 52 cents, or 0.63%, to $82.51 a barrel at 0721 GMT, after a 1.5% jump in the previous session. U.S. West Texas Intermediate (WTI) crude futures rose 57 cents, or 0.72%, to $80.03 a barrel, extending a 2.1% gain in the previous session.

Brent and WTI were on track for a more than 6% gain in the first week of the year, with prices at their highest since late November, as supply concerns overtook worries that the rapid spread of the Omicron coronavirus variant might hurt demand.

"The upward jump in oil prices mostly reflects the market jitters as unrest escalates in Kazakhstan and the political situation in Libya continues to deteriorate and sideline oil output," Rystad Energy analyst Louise Dickson said in emailed comments.

After days of unrest in Kazakhstan, during which the government declared a state of emergency, Russia on Thursday sent in paratroopers to quash the uprising.

The protests began in Kazakhstan's oil-rich western regions after state price caps on butane and propane were removed on New Year's Day.

Meanwhile, supply additions from the Organization of the Petroleum Exporting Countries, Russia and allies, together called OPEC+, are not keeping up with demand growth.

OPEC's output in December rose by 70,000 barrels per day from the previous month, versus the 253,000 bpd increase allowed under the OPEC+ supply deal, which restored output that was slashed in 2020 when demand collapsed under COVID-19 lockdowns.

Production in Libya has dropped to 729,000 barrels per day, down from a high of 1.3 million bpd last year, partly due to pipeline maintenance work.

While the Omicron variant is rapidly taking hold, demand-side concerns are easing amid rising evidence that it is less severe than previous variants and as governments employ generally less rigid containment measures in response to it, analysts from Fitch Solutions said in a note.

Wang Xiao, lead researcher from Guotai Junan Futures, said that low oil inventory in Europe and America was also supporting market sentiment. "But overall, the price rally stokes inflation concerns, which could weigh on any further oil price gains."