U.S. crude for January delivery rose 28 cents to $70.95 a barrel by 1537 GMT (10:37 a.m. EST), after losing almost $2 in its sixth straight day of losses on Wednesday, when it hit the lowest since early October at $70.13.
London Brent crude fell 8 cents to $72.31.
I think today we are seeing a pause after the previous day's sharp losses, Carsten Fritsch, oil analyst at Commerzbank in Frankfurt said on Thursday.
The $70 level is holding for now but I think there is more downside potential further forward.
U.S. jobs data helped to lift stock markets both sides of the Atlantic on Thursday, aiding oil's rally as investors moved to riskier assets.
Oil prices dropped on Wednesday after U.S. Energy Information Administration data showed builds in U.S. refined product stocks, highlighting the weakness of demand in the world's largest energy consumer.
There were further signs that global oil supplies were rising on Thursday as Saudi Arabia restored full term crude allocations to at least two Asian buyers for January and kept contracted volumes to six others, according to industry sources.
However, the world's top oil exporter will keep crude oil supplies to customers in Europe unchanged in January compared to December.
The spread between front-month Brent and U.S. crude oil futures widened to around $2 a barrel on Thursday, stretched by the build in stocks at Cushing, Oklahoma, the delivery point for U.S. crude oil futures.
For a graphic of Brent versus U.S. crude, which also shows the spread between the first and second U.S. crude futures months and the level of crude oil stocks at Cushing, click here
Despite the drop in overall crude stocks, inventories at Cushing are approaching the record high in February, widening the spread between Brent and WTI (U.S. crude), Fritsch said.
The EIA data on Wednesday showed crude stocks at Cushing were up last week by 2.5 million barrels at 33.4 million barrels, near the 35 million-barrel peak hit in February.
Saudi Arabia's move to restore full term crude supply to two Asian buyers comes ahead of OPEC's December 22 meeting at which most members have said they will not raise production targets.
Ecuador's energy minister on Wednesday said he expected OPEC to leave oil output targets unchanged at the meeting, setting the stage for prices to remain between $70 and $80 per barrel.
(Editing by James Jukwey, editing by Anthony Barker)